Representations of Parabolic and Borel Subgroups
نویسنده
چکیده
We demonstrate a relationships between the representation theory of Borel subgroups and parabolic subgroups of general linear groups. In particular, we show that the representations of Borel subgroups could be computed from representations of certain maximal parabolic subgroups.
منابع مشابه
Computing Orbits of Minimal Parabolic k-subgroups Acting on Symmetric k-varieties
The orbits of a minimal parabolic k-subgroup acting on a symmetric k-variety are essential to the study of symmetric k-varieties and their representations. This paper gives an algorithm to compute these orbits and most of the combinatorial structure of the orbit decomposition. There are several ways to describe these orbits, see for example [22, 28, 35]. Fundamental in all these descriptions ar...
متن کاملEmerton’s Jacquet Functors for Non-Borel Parabolic Subgroups
This paper studies Emerton’s Jacquet module functor for locally analytic representations of p-adic reductive groups, introduced in [Eme06a]. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for the derived subgroup ofM gives rise to essentially admissible locally analytic representations of the torus Z(M), which have a natural...
متن کاملMath 7310 Fall 2010: Introduction to Geometric Representation Theory
1. Spaltenstein’s theorem and Hotta’s construction 1 2. Equivariant cohomology and divided differences 5 3. Review of: Borel subgroups, parabolic subgroups, the Bruhat decomposition 10 4. The Steinberg scheme 12 5. Algebras of constructible correspondences 13 6. Hall algebras 17 7. Geometric construction of Uq(n+) for simply-laced Lie algebras 20 8. Convolution in Borel-Moore homology 23 9. Gro...
متن کاملThe residual spectrum of $U(n,n)$; contribution from Borel subgroups
In this paper we study the residual spectrum of the quasi-split unitary group $G=U(n,n)$ defined over a number field $F$, coming from the Borel subgroups, $L_{dis}^2(G(F)backslash G(Bbb A))_T$. Due to lack of information on the local results, that is, the image of the local intertwining operators of the principal series, our results are incomplete. However, we describe a conjec...
متن کاملTwo-sided Bgg Resolutions of Admissible Representations
We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions of G-integrable admissible representations of affine Kac-Moody algebras at fractional levels. As an application we establish the semi-infinite analogue of the generalized Borel-Weil theorem for minimal parabolic subalgebras which enables an inductive study of admissible representations.
متن کامل