Authors: Pavle Pandžić, Vladimír Souček Journal of Mathematical Physics 58, 111512 (2017); https://doi.org/10.1063/1.4986121 Abstract: We give a geometric construction of the Bernstein-Gel’fand-Gel’fand (BGG) resolutions in singular infinitesimal character in the case of 1-graded complex Lie algebras of type A.
Authors: Pavle Pandžić, Petr Somberg Journal of Mathematical Physics 58, 041702 (2017); https://doi.org/10.1063/1.4979623 Abstract: We introduce a Dirac operator for the quantum group , as an element of the tensor product of with the Clifford algebra on two generators. We study the properties of , including an analogue of Vogan’s conjecture. We compute the cohomology […]
Authors: Jing-Song Huang, Pavle Pandžić, David Vogan Science China Mathematics, November 2017, Volume 60, Issue 11, pp 1937–1962. https://doi.org/10.1007/s11425-017-9097-8 Abstract: Let be a connected real reductive group with maximal compact subgroup of the same rank as . Dirac cohomology of an module can be identified with a geometric object—the -dominant part of a face of the convex hull […]
Author: Ana Prlić Glasnik Matematički, Vol. 52, No. 2 (2017), 275-288. DOI: 10.3336/gm.52.2.07 Abstract. Let be the Lie group , with maximal compact subgroup . Let be the complexification of the Lie algebra of , and let be the universal enveloping algebra of . Let be the Cartan decomposition of , […]