# (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, p. 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), Trans. 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, http://xxx.lanl.gov/abs/1002.1053.

Loebl M., Somberg P., Graphs critically embedded on Riemann surfaces and Ihara-Selberg zeta functions: genus one case, 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, http://xxx.lanl.gov/abs/1006.5707.

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 rules, tensor products and singular vectors for generalized Verma modules I., 2010, preprint.

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, http://xxx.lanl.gov/abs/1110.5425.

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, http://xxx.lanl.gov/abs/1209.3970.

Coulembier K., Somberg P., Soucek V., Joseph-like ideals and harmonic analysis for osp(m|2n), International Math. Research Not., http://imrn.oxfordjournals.org/content/early/2013/04/22/imrn.rnt074.abstract

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 ${\mathbb R}^2$, http://xxx.lanl.gov/abs/1301.2682.

Milev T., Somberg P., The F-method and a branching problem for generalized Verma modules associated to $({\LieGtwo},{so(7)})$, http://arxiv.org/abs/1303.7311, 2013. .

Pandzic P., Somberg P., Higher Dirac cohomology of modules with generalized infinitesimal character, 2013, preprint.

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