Unit for Representation Theory of Lie Algebras, Number Theory, and Related Structures

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 , […]

Authors: Dražen Adamović, Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše Japanese Journal of Mathematics, September 2017, Volume 12, Issue 2, pp 261–315. https://doi.org/10.1007/s11537-017-1621-x Abstract: We present methods for computing the explicit decomposition of the minimal simple affine W-algebra  as a module for its maximal affine subalgebra  at a conformal level k, that is, whenever the Virasoro vectors of  and  coincide. A particular emphasis […]