𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Finite-dimensional representations of invariant differential operators

✍ Scribed by Gerald W. Schwarz

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
362 KB
Volume
258
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a reductive complex algebraic group and V a finite-dimensional G-module.

be restriction, where D(O(V ) G ) denotes the differential operators on O(V ) G . Much attention of late has been given to the study of Im ρ and Ker ρ. Less well studied are properties of B itself. For example:

• What is the representation theory of B? What are the primitive ideals of B?

• Does B have finite-dimensional representations? In particular, is B an FCR algebra?

Little is known about these questions when G is noncommutative. We give answers for the adjoint representation of SL 3 (C), already an interesting and difficult case.

📜 SIMILAR VOLUMES

Finite-dimensional representations of in
Finite-dimensional representations of invariant differential operators, II
✍ Gerald W. Schwarz 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 97 KB

In Part I of this paper [G.W. Schwarz, Finite-dimensional representations of invariant differential operators, J. Algebra 258 (2002) 160-204] we considered the representation theory of the algebra B := D(g) G , where G = SL 3 (C) and D(g) G denotes the algebra of G-invariant polynomial differential

Invariant Algebra and Cuspidal Represent
Invariant Algebra and Cuspidal Representations of Finite Monoids
✍ Mohan S Putcha 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 120 KB

Motivated by the theories of Hecke algebras and Schur algebras, we consider in this paper the algebra ‫ރ‬ M G of G-invariants of a finite monoid M with unit group G. If M is a regular ''balanced'' monoid, we show that ‫ރ‬ M G is a quasi-hereditary algebra. In such a case, we find the blocks of ‫ރ‬ M