(P)reprints and publications


P. Pandzic, P. Somberg, Braided coproduct, antipode and adjoint action for $U_q(sl_2)$, accepted to Archivum Math., https://arxiv.org/abs/2404.06871.

P. Hu, D. Kriz, I. Kriz, P. Somberg, Some remarks on plectic motivic spaces and spectra, preprint, 2023.

R. O. Buachalla, P. Somberg, Lusztig's Quantum Root Vectors and a Dolbeault Complex for the A-Series Full Quantum Flag Manifolds, preprint, 2023, https://arxiv.org/abs/2312.13493.

P. Hu, I. Kriz, B. Riley, P. Somberg, New variants of the Adams-Novikov spectral sequence and an algebraic computation of self-conjugate cobordism, preprint, 2023.

P. Hu, I. Kriz, P. Somberg, F. Zou, Equivariant operations in topological Hochschild homology, preprint, 2023.

P. Hu, I. Kriz, G. Li, P. Somberg, F. Zou, The Z/p-equivariant spectrum BPR for an odd prime p, preprint, 2023.

B. Das, R. O. Buachalla, P. Somberg, Spectral gaps for twisted Dolbeault--Dirac operators over the irreducible quantum flag manifolds, https://arxiv.org/abs/2206.10719, preprint, 2022.

P. Hu, I. Kriz, P. Somberg, F. Zou, The Z/p-equivariant dual Steenrod algebra for an odd prime p, https://arxiv.org/abs/2205.13427, preprint, 2022.

F. D. Garcia, A. Krutov, R. O. Buachalla, P. Somberg, K. R. Strung, Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds, Lett. Math. Phys. 111, 10 (2021), https://doi.org/10.1007/s11005-020-01340-7 (Lett Math Phys 111, 23 (2021). https://doi.org/10.1007/s11005-021-01363-8).

P. Somberg, P. Zima, Killing spinor-valued forms and their integrability conditions, Annals of Global Analysis and Geometry (2020), https://doi.org/10.1007/s10455-020-09730-9, (grant no corrigendum: https://link.springer.com/article/10.1007/s10455-021-09761-w)

F. D. Garcia, A. Krutov, R. O. Buachalla, P. Somberg, K. R. Strung, Positive Line Bundles Over the Irreducible Quantum Flag Manifolds, Lett Math Phys 112, 123 (2022), https://doi.org/10.1007/s11005-022-01619-x.

B. Das, R. O. Buachalla, P. Somberg, A Dolbeault-Dirac Spectral Triple for Quantum Projective Space, Doc. Math. 25, 1079-1157 (2020), DOI: 10.25537/dm.2020v25.1079-1157, https://arxiv.org/abs/1903.07599.

B. Das, R. O. Buachalla, P. Somberg, Compact Quantum Homogeneous Kahler Spaces, https://arxiv.org/abs/1910.14007, preprint 2019/2022.

Hu P., Kriz I., Somberg P., Equivariant formal group laws and complex-oriented spectra over primary cyclic groups: elliptic curves, Barsotti-Tate groups, and other examples, J. Homotopy Relat. Struct. 16, 635-665 (2021). https://doi.org/10.1007/s40062-021-00291-7

Hu P., Kriz I., Somberg P., On the equivariant motivic filtration of the topological Hochschild homology of polynomial algebras, Advances in Mathematics, Volume 412, 108803, 2023, https://doi.org/10.1016/j.aim.2022.108803, https://arxiv.org/abs/2211.12381 .

Hu P., Kriz I., Somberg P., Tate cohomology of connected K-theory for elementary abelian groups revisited, Journal of homotopy and related structures, 2019, https://doi.org/10.1007/s40062-018-00229-6, https://link.springer.com/article/10.1007/s40062-018-00229-6 .

Somberg P., Silhan J., Higher symmetries of symplectic Dirac operator, Geom. Dedicata (2020), 1-22, https://doi.org/10.1007/s10711-020-00529-3, https://arxiv.org/abs/1803.06970.

Barchini L., Somberg P., Trapa P. E., Reducible characteristic cycles of Harish Chandra modules for U(p,q) and the Kashiwara-Saito singularity, Communications in Algebra, 2019, https://doi.org/10.1080/00927872.2019.1596280, https://www.tandfonline.com/doi/full/10.1080/00927872.2019.1596280.

Fischmann M., Orsted B., Somberg P., Bernstein-Sato identities and conformal symmetry breaking operators, Journal of Funct. Anal. Volume 277, Issue 11 (2019), 108219, https://doi.org/10.1016/j.jfa.2019.04.002.

Hu P., Kriz I., Somberg P., On some adjunctions in equivariant stable homotopy theory, Algebraic & Geometric Topology 18-4 (2018), 2419-2442. DOI 10.2140/agt.2018.18.2419 .

Pandzic P., Somberg P., Dirac operator and its cohomology for the quantum group $U_q(sl_2)$, Journal of Mathematical Ph. 58, 041702 (2017), http://dx.doi.org/10.1063/1.4979623, https://arxiv.org/abs/1702.02435.

Krizka L., Somberg P., Conformal Galilei algebras, symmetric polynomials and singular vectors, Letters Math. Phys. (2017), https://doi.org/10.1007/s11005-017-0997-0.

Futorny S., Krizka L., Somberg P., Geometric realizations of affine Kac-Moody algebras, Journal of Algebra, Volume 528, 2019, 177-216, https://doi.org/10.1016/j.jalgebra.2019.03.011.

Hu P., Kriz I., Somberg P., Derived representation theory and stable homotopy categorification of sl_k, Advances in Math. 341, 367-439, 2019, https://doi.org/10.1016/j.aim.2018.10.044, https://www.sciencedirect.com/science/article/pii/S0001870818304389.

Somberg P., Zima P., Killing spinor-valued forms and the cone construction, Archivum Mathematicum 52, 2031-2044, DOI 10.5817/AM2016-5-2031, 2016, http://arxiv.org/abs/1605.06947.

Fischmann M., Juhl A., Somberg P., Conformal symmetry breaking differential operators on differential forms, Memoirs of AMS, 2020, Volume 268, Number 1304, ISBNs: 978-1-4704-4324-5 (print); 978-1-4704-6339-7 (online), DOI: https://doi.org/10.1090/memo/1304, http://arxiv.org/abs/1605.04517, 2016.

Holikova M., Krizka L., Somberg P., Projective structure, $\widetilde{\mathrm{SL}}(3,{\mathbb R})$ and the symplectic Dirac operator, Archivum Mathematicum, 52 (2016), 2041-2052, DOI: 10.5817/AM2016-5-2041, http://arxiv.org/abs/1604.04376.

Krizka L., Somberg P., Equivariant differential operators on spinors in conformal geometry, Complex Variables and Elliptic Equations, 2016, http://www.tandfonline.com/doi/full/10.1080/17476933.2016.1234461, http://arxiv.org/abs/1602.01403.

Krizka L., Somberg P., Differential invariants on symplectic spinors in contact projective geometry, Journal of Mathematical Ph. 58, 091701 (2017), http://dx.doi.org/10.1063/1.5001032.

De Bie H., Holikova M., Somberg P., Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator, Advances in Applied Clifford Algebras 26, 1-30, DOI 10.1007/s00006-016-0696-4, 2016, http://arxiv.org/abs/1511.04189 .

Fischmann M., Somberg P., The Boundary Value Problem for Laplacian on Differential Forms and Conformal Einstein Infinity, Journal of Generalized Lie Theory Appl. 11: 256, 2017, DOI:10.4172/1736-4337.1000256, http://arxiv.org/abs/1508.01511, 2015.

Krizka L., Somberg P., On the composition structure of twisted Verma modules for the Lie algebra sl(3,C), Archivum Mathematicum 51 (2015), 299-314, http://arxiv.org/abs/1509.00646.

Pandzic P., Somberg P., Branching problems and sl(2,C)-actions, Archivum Mathematicum 51 (2015), 315-330, http://arxiv.org/abs/1511.03048.

Krizka L., Somberg P., Algebraic analysis on scalar generalized Verma modules of Heisenberg parabolic type I.: An-series, Transformation Groups, 2017, DOI: 10.1007/s00031-016-9414-5, http://xxx.lanl.gov/abs/1502.07095.

Fischmann M., Krattenthaler Ch., Somberg P., On Conformal Powers of the Dirac Operator on Einstein Manifolds, Math. Zeit., DOI 10.1007/s00209-015-1450-7, http://xxx.lanl.gov/abs/1405.7304, 2014.

Michel J. P., Somberg P., Silhan J., Prolongation of symmetric Killing tensors and commuting symmetries of the Laplace operator, Rocky Mountain Journal of Mathematics, Volume 47, Number 2, 2017, DOI:10.1216/RMJ-2017-47-2-1, http://xxx.lanl.gov/abs/1403.7226.

Fischmann M., Somberg P., Residue Family Operators on Spinors and Spectral Theory of Dirac operator on Poincare-Einstein Spaces, http://xxx.lanl.gov/abs/1402.03362013, 2014.

Hu P., Kriz I., Somberg P., Equivariant K-theory of compact Lie groups with involution, Journal of K-Theory, volume 13, issue 02, pp. 313-335, doi:10.1017/is014002004jkt254, http://arxiv.org/abs/1401.7827, 2013.

Barchini L, Somberg P., On the Unitary Globalization of Cohomologically Induced Modules, Journal of Functional Analysis, Volume 266, Issue 6, 2014, 3840-3854, http://dx.doi.org/10.1016/j.jfa.2013.10.006.

Pandzic P., Somberg P., Higher Dirac cohomology of modules with generalized infinitesimal character, Transformation Groups, Volume 21, Issue 3, 803-819, 2016, http://xxx.lanl.gov/abs/1310.3570.

Milev T., Somberg P., The F-method and a branching problem for generalized Verma modules associated to $({\LieGtwo},{so(7)})$, Archivum Math. Volume 49 (2013), No. 5, pp. 317-332, http://arxiv.org/abs/1303.7311, 2013.

Dostalova M., Somberg P., Symplectic twistor operator and its solution space on ${\mathbb R}^{2n}$, Complex Analysis and Operator Theory 4, 2013, http://link.springer.com/article/10.1007%2Fs11785-013-0300-z.

Dostalova M., Somberg P., Symplectic twistor operator and its solution space on ${\mathbb R}^2$, Archivum Math. Volume 49 (2013), No. 3, 161-185, http://xxx.lanl.gov/abs/1301.2682.

Somberg P., Rankin-Cohen brackets for orthogonal Lie algebras and bilinear conformally invariant differential operators, http://xxx.lanl.gov/abs/1301.2687, to appear in Kobayashi Festschrift, Springer.

Somberg P., Finite reflection groups, conformal geometry and the conformal Dunkl-Laplace differential-difference operators, Differential Geometry and its Applications 31, 2013, 166-174.

Coulembier K., Somberg P., Soucek V., Joseph-like ideals and harmonic analysis for osp(m|2n), International Mathematics Research Notices, Volume 2014, Issue 15, 2014, 4291-4340, https://doi.org/10.1093/imrn/rnt074 .

Milev T., Somberg P., The branching problem for generalized Verma modules, with application to the pair $(so(7),Lie G_2)$, extended version with tables, Journal of Algebra and its Applications, Vol. 13 No. 07 1450034, 2014, http://xxx.lanl.gov/abs/1209.3970 .

Kriz I., Loebl M., Somberg P., On discrete field theory properties of the dimer and Ising models and their conformal field theory limits, Journal of Math. Phys. 54, 053513, 2013, http://dx.doi.org/10.1063/1.4807308 .

Eastwood M. G., Somberg P., Soucek V., Universal splitting operators for general parabolic geometries, 2011, preprint.

Eastwood M. G., Somberg P., Soucek V., Symmetries of Dirac operator, 2010, preprint.

Oersted B., Somberg P., Soucek V., Analytic realization of translation functor - the case of spinor representation, 2010, preprint.

Kobayashi T., Oersted B., Somberg P., Soucek V., Branching rules, tensor products and singular vectors for generalized Verma modules II., 2010, preprint.

Kobayashi T., Oersted B., Somberg P., Soucek V., Branching laws for Verma modules and applications in parabolic geometry. I, Advances in Mathematics 285 (2015) 1-57, Archive http://xxx.lanl.gov/abs/1305.6040.

Somberg P., Homomorphisms of generalized Verma modules, BGG parabolic category ${\fam2 O}^\gop$ and Juhl's conjecture, Journal of Lie theory, Volume 22, No. 2, 2012, 541-555.

Hong Van Le, Somberg P., Vanzura J., Poisson smooth structures on stratified symplectic spaces, Proceedings of the 6-th World Conference on 21st Century Mathematics, http://xxx.lanl.gov/abs/1006.5707, http://link.springer.com/book/10.1007%2F978-3-0348-0859-0 .

Hong Van Le, Somberg P., Vanzura J., Smooth structures on pseudomanifolds with isolated conical singularities, Acta Mathematica Vietnamica, 2013, Volume 38, Issue 1, pp 33-54, http://xxx.lanl.gov/abs/1006.5707.

Hammerl M., Somberg P., Soucek V., Silhan J., Invariant prolongation of overdetermined PDEs in projective, conformal and Grassmannian geometry, Annals of Global Analysis and Geometry, DOI: 10.1007/s10455-011-9306-9, 2012, Volume 42, Issue 1, pp 121-145.

Hammerl M., Somberg P., Soucek V., Silhan J., On a new normalization for tractor covariant derivatives, Journal of European Mathematical Society, Vol 14, No 6, 2012 1859-1883.

Loebl M., Somberg P., Graphs critically embedded on Riemann surfaces and Ihara-Selberg zeta functions: genus one case, The Electronic Journal of Combinatorics, Volume 22, Issue 1 (2015), http://xxx.lanl.gov/abs/0912.3200.

D. Bie H., Somberg P., Soucek V., The Howe duality and polynomial solutions for symplectic Dirac operator, Journal of Geometry and Physics 75, 2014, 120-128.

D. Bie H., Oersted B., Somberg P., Soucek V., The Clifford Deformation of the Hermite Semigroup, Symmetry, Integrability and Geometry:SIGMA, 9, 2013, 010, 22 pages, http://dx.doi.org/10.3842/SIGMA.2013.010.

D. Bie H., Oersted B., Somberg P., Soucek V., Dunkl operators and a family of realizations of osp(2|1), Transactions of Amer. Math. Soc. 364, 2012, 3875-3902.

Somberg P., Killing spinor-forms and its applications in Riemannian geometry, Hypercomplex Analysis and its Applications, Trends in Mathematics, Birkhauser, 2011, 233--247, Birkhauser.

Oersted B., Somberg P., Soucek V., The Howe duality for the Dunkl version of the Dirac operator, Advances in Applied Clifford Algebras, Volume 19, Number 2, 2009, 403-415.

Somberg P., Deformations of quadratic algebras, the Joseph ideal for classical Lie algebras, and special tensors, Symmetries and overdetermined systems of partial differential equations, Springer, New York, The IMA volumes in Math. and its Appl., USA (2007) p. 527-537.

Gover R., Somberg P., Soucek V., Yang-Mills detour complexes and conformal geometry, Communications in Mathematical Physics, Springer Berlin/Heidelberg, Volume 278, Number 2 (2008) 307-327.

Eastwood M.G., Somberg P., Soucek V., Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras, Journal of Geom. and Phys. 57, 2007, 2539-2546.

Somberg P., Conformal Killing forms via cup product on twistor spinors for conformal Berstein-Gelfand-Gelfand sequence, Adv. Appl. Clifford Alg., Vol. 19, Num. 3-4, (2009), 947-957.

Somberg P., Hasse graphs and parabolic subalgebras of exceptional Lie algebra f_4, Suppl. ai Rend. del Circ. Matematico di Pal., Ser. II, Num. 75, 2005.

Somberg P., Higher Monogenicity and Residue Theorem for Rarita-Schwinger (and Higher Spin) operators, Suppl. ai Rend. del Circ. Matematico di Pal., Ser. II, Num. 72, 2004.

Somberg P., The Generalized A_\infty -Algebra Structure on BGG Sequences and Generalized Associative operad, Suppl. ai Rend. del Circ. Matematico di Pal., Ser. II, Num. 71, 2003.

Somberg P., Crystallizing patterns of BGG sequences, Suppl. ai Rend. del Circ. Matematico di Pal., Ser. II, Num. 69, 2002.

Somberg P., On the passage from orthogonal(conformal) to symplectic(contact) from the point of view of spinor theory, Mathematical Publications, Vol. 3, Differential Geometry and Its Applications, 2002.

Somberg P., Quaternionic Complexes in Clifford Analysis, NATO Science Series in Mathematics Physics and Chemistry, Vol. 25, Clifford Analysis And Applications, 2001.

Somberg P., Non-standard Singular Invariant Differential Operators for Quaternionic Parabolic Geometries - Beyond the $A_n$-series of Lie Algebras, Advances In Applied Clifford Algebras - Clifford Analysis and Related Topics, ISSN 0188-7009, Vol 11 (S2), 2001.

Somberg P., Generalized Penrose Transform in Representation Theory - Non-standard Invariant Morphisms for Parabolic Geometries (after R.J.Baston), Martina Franca (2000).

Somberg P., Twistor Operators on Conformally Flat Spaces, Suppl. ai Rend. del Circ. Matematico di Pal., Ser. II, Num. 66, 2001.

Somberg P., BGG Sequences on Spheres, Comm. Math. Univ. Car. 41 (3), 2000.

Somberg P., The Properties of BGG Resolution on the Spheres, Dissertation work, Charles University, Prague 1999.