[图书][B] Dirac operators in representation theory
JS Huang, P Pandzic - 2007 - books.google.com
This monograph presents a comprehensive treatment of important new ideas on Dirac
operators and Dirac cohomology. Dirac operators are widely used in physics, differential …
operators and Dirac cohomology. Dirac operators are widely used in physics, differential …
Dirac operators in representation theory
JS Huang, P Pandžić - Representations of real and p-adic groups, 2004 - World Scientific
Vogan's conjecture on Dirac cohomology reveals an algebraic nature of Dirac operators. In
these notes we explain our proof of the Vogan's conjecture. As applications we describe …
these notes we explain our proof of the Vogan's conjecture. As applications we describe …
Dirac cohomology of some Harish-Chandra modules
JS Huang, YF Kang, P Pandžić - Transformation groups, 2009 - Springer
In this paper we determine the Dirac cohomology of certain irreducible Harish-Chandra
modules of a semisimple connected Lie group G with finite center: irreducible finite …
modules of a semisimple connected Lie group G with finite center: irreducible finite …
Dirac cohomology, elliptic representations and endoscopy
JS Huang - Representations of Reductive Groups: In Honor of the …, 2015 - Springer
Abstract The first part (Sections 2–7) of this paper is a survey of some of the recent
developments in the theory of Dirac cohomology, especially the relationship of Dirac …
developments in the theory of Dirac cohomology, especially the relationship of Dirac …
[PDF][PDF] Dirac cohomology of unipotent representations of Sp (2n, R) and U (p, q)
D Barbasch, P Pandžić - arXiv preprint arXiv:1302.2503, 2013 - arxiv.org
arXiv:1302.2503v2 [math.RT] 19 Feb 2013 Page 1 arXiv:1302.2503v2 [math.RT] 19 Feb 2013
July 16, 2018 DIRAC COHOMOLOGY OF UNIPOTENT REPRESENTATIONS OF Sp(2n, R) …
July 16, 2018 DIRAC COHOMOLOGY OF UNIPOTENT REPRESENTATIONS OF Sp(2n, R) …
Dirac series for E6 (− 14)
LG Ding, CP Dong, H He - Journal of Algebra, 2022 - Elsevier
Up to equivalence, this paper classifies all the irreducible unitary representations with non-
zero Dirac cohomology for the simple Lie group E 6 (− 14), which is of Hermitian symmetric …
zero Dirac cohomology for the simple Lie group E 6 (− 14), which is of Hermitian symmetric …
Twisted Dirac index and applications to characters
D Barbasch, P Pandžić - Affine, Vertex and W-algebras, 2019 - Springer
We present recent joint work with Peter Trapa on the notion of twisted Dirac index and its
applications to (twisted) characters and to extensions of modules in a short and informal …
applications to (twisted) characters and to extensions of modules in a short and informal …
Dirac index and twisted characters
D Barbasch, P Pandžić, P Trapa - Transactions of the American …, 2019 - ams.org
Let $ G $ be a real reductive Lie group with maximal compact subgroup $ K $. We
generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in …
generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in …
Dirac cohomology of highest weight modules
JS Huang, W Xiao - Selecta Mathematica, 2012 - Springer
We show that the Dirac cohomology coincides with nilpotent Lie algebra (co) homology up
to a twist of a one-dimensional character for simple highest weight modules. As a …
to a twist of a one-dimensional character for simple highest weight modules. As a …
Dirac cohomology, K-characters and branching laws
JS Huang, P Pandžić, F Zhu - American journal of mathematics, 2013 - muse.jhu.edu
Inspired by work of Enright and Willenbring, we prove a generalized Littlewood's restriction
formula in terms of Dirac cohomology. Our approach is to use a character formula of …
formula in terms of Dirac cohomology. Our approach is to use a character formula of …