(P)reprints and publications



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

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

Somberg P., Twistor Operators on Conformally Flat Spaces, Suppl. ai Rend. del Circ. Matematico di Pal., Ser. II, Num. 66, 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., 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., Quaternionic Complexes in Clifford Analysis, NATO Science Series in Mathematics Physics and Chemistry, Vol. 25, Clifford Analysis And Applications, 2001.

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

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., 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., 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., 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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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 .

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.

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.

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

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

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

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

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 .

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 .

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, 42914340, https://doi.org/10.1093/imrn/rnt074 .

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

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

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.

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.

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.

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.

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.

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.

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.

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., 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.

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.

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., 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.

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.

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 .

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.

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.

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.

Fischmann M., Juhl A., Somberg P., Conformal symmetry breaking differential operators on differential forms, Memoirs of AMS, 2018, http://arxiv.org/abs/1605.04517, 2016.

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.

Hu P., Kriz I., Somberg P., Derived representation theory and stable homotopy categorification of sl_k, available at http://www.math.lsa.umich.edu/~ikriz/drt16084.pdf, preprint 2016.

Futorny S., Krizka L., Somberg P., Geometric realizations of affine Kac-Moody algebras, http://arxiv.org/abs/1610.07973, preprint 2016.

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.

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.

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 .

Fischmann M., Orsted B., Somberg P., Bernstein-Sato identities and conformal symmetry breaking operators, https://arxiv.org/abs/1711.01546, preprint 2017.

Barchini L., Somberg P., Trapa P. E., Reducible characteristic cycles of Harish Chandra modules for U(p,q) and the Kashiwara-Saito singularity, https://arxiv.org/abs/1801.03465, preprint 2018.

Somberg P., Silhan J., Higher symmetries of symplectic Dirac operator, https://arxiv.org/abs/1803.06970, preprint 2018.

Hu P., Kriz I., Somberg P., Tate cohomology of connected K-theory for elementary abelian groups revisited, preprint 2018.

Hu P., Kriz I., Somberg P., On the equivariant motivic filtration of the topological Hochschild homology of polynomial algebras, preprint 2018.