Computing the associated cycles of certain Harish-Chandra modules
| Autor: | Salah Mehdi, Roger Zierau, Pavle Pandžić, David A. Vogan |
|---|---|
| Přispěvatelé: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [University of Zagreb], University of Zagreb, Department of Mathematics [MIT], Massachusetts Institute of Technology (MIT), Oklahoma State University [Stillwater], The second named author was supported by grant no. 4176 of the Croatian Science Foundation and by the QuantiXLie Centre of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme (KK.01.1.1.01.0004)., The third named author was supported in part by NSF grant DMS 0967272 |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Polynomial Rank (linear algebra) General Mathematics Nilpotent orbit 01 natural sciences associated variety associated cycle nilpotent orbit 0101 mathematics [MATH]Mathematics [math] Linear combination Mathematics::Representation Theory Mathematics Mathematics::Combinatorics 010102 general mathematics Dirac index Cartan subalgebra Lie group 16. Peace & justice ( K)-module Dirac cohomology Dirac index nilpotent orbit associated variety associated cycle Springer correspondence 010101 applied mathematics ( Springer correspondence Dirac cohomology 2010 Mathematics Subject Classification. Primary 22E47 Secondary 22E46 Maximal compact subgroup |
| Zdroj: | Glasnik matematički Volume 53 Issue 2 Glasnik Matematicki Glasnik Matematicki, Drazen Adamovic, 2018, 53 (2), pp.275-330. ⟨10.3336/gm.53.2.05⟩ |
| ISSN: | 1846-7989 0017-095X |
| DOI: | 10.3336/gm.53.2.05⟩ |
| Popis: | International audience; Let G_R be a simple real linear Lie group with maximal compact subgroup K_R and assume that rank(G_R) = rank(K_R). In [MPVZ] we proved that for any representation X of Gelfand-Kirillov dimension 1 2 dim(G_R /K_R), the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing X is a linear combination, with integer coefficients, of the multiplicities of the irreducible components occurring in the associated cycle. In this paper we compute these coefficients explicitly. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|