Naslov
Dirac cohomology for Harish-Chandra modules

Autori
Huang, Jing-Song ; Pandžić, Pavle ; Renard, David

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Abstracts of the "Enveloping Algebras and Geometric Representation Theory" ; u: Oberwolfach Report 13 (2005) / Kumar, Shrawan ; Littelman, Peter: Soergel, Wolfgang - Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2005, 746-749

Skup
Enveloping Algebras and Geometric Representation Theory

Mjesto i datum
Oberwolfach, Njemačka, 13.03.2005. - 19.03.2005

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
reductive group; representation; Harish-Chandra module; Dirac operator; Dirac cohomology; Lie algebra cohomology

Sažetak
Let G be a connected reductive Lie group with a maximal compact subgroup K corresponding to a Cartan involution. Let g=k+p be the corresponding Cartan decomposition of the complexified Lie algebra of G. Let D be the Dirac operator for (g, K) ; it is an element of the algebra U(g)\tensor C(p). If X is a Harish-Chandra module for (g, K), the Dirac cohomology of X is the kernel of D on X tensored by the spin module S for C(p), divided by the intersection of the kernel and the image of D. We show that if (g, K) is a Hermitian symmetric pair, then the Dirac cohomology of a unitary module X is very closely related to the Lie algebra cohomology with respect to p^+. Similar results hold in the case of a parabolic subalgebra q=l+u with l contained in k and u containing p^+: Now the Dirac cohomology with respect to Kostant's cubic Dirac operator corresponding to l is closely related to u-cohomology.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Rad je kao pozvano predavanje prezentiran i na skupu 2007 Nankai Summer School Representation Theory and Harmonic Analysis, održanom od 10.-21.06.2007., Tianjin, Kina.

POVEZANOST RADA