## 532 Citations

### Contravariant forms on Whittaker modules

- MathematicsProceedings of the American Mathematical Society
- 2020

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### Introduction to W-Algebras and Their Representation Theory

- Mathematics
- 2017

These are lecture notes from author’s mini-course on W-algebras during Session 1: “Vertex algebras, W-algebras, and application” of INdAM Intensive research period “Perspectives in Lie Theory”, at…

### W-algebras and Whittaker categories

- Mathematics
- 2016

Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's…

### Annihilator varieties, adduced representations, Whittaker functionals, and rank for unitary representations of GL(n)

- Mathematics
- 2011

In this paper, we study irreducible unitary representations of $${GL_{n}(\mathbb{R})}$$ and prove a number of results. Our first result establishes a precise connection between the annihilator of a…

### The Algebraic Integrability of the Quantum Toda Lattice and the Radon Transform

- Mathematics
- 2009

AbstractWe study the maximal commutative ring of partial differential operators which includes the quantum completely integrable system defined by the quantum Toda lattice. Kostant shows that the…

### On Whittaker modules over a class of algebras similar to U(sl2)

- Mathematics
- 2006

Motivated by the study of invariant rings of finite groups on the first Weyl algebras A1 and finding interesting families of new noetherian rings, a class of algebras similar to U(sl2) was introduced…

### Representation Theory of W-Algebras

- Mathematics
- 2005

This paper is the detailed version of math.QA/0403477 (T. Arakawa, Quantized Reductions and Irreducible Representations of W-Algebras) with extended results;
We study the representation theory of…

### Representation theory and quantum inverse scattering method: the open Toda chain and the hyperbolic Sutherland model

- Mathematics
- 2002

Using the representation theory of Gl(N), we express the wave function of the GL(N,ℝ) Toda chain, which was recently obtained by two of us by the quantum inverse scattering method, in terms of…

## References

SHOWING 1-10 OF 19 REFERENCES

### The Multiplicity One Theorem for GL n

- Mathematics
- 1974

The purpose of this paper is to establish preliminary results in the theory of representations in the direction of a systematic treatment of Hecke-theory for the group GLn. In particular, special…

### Finite- and infinite-dimensional representation of linear semisimple groups

- Mathematics
- 1973

Every representation in the nonunitary principal series of a noncompact connected real semisimple linear Lie group G with maximal compact subgroup K is shown to have a /C-finite cyclic vector. This…

### The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group

- Mathematics
- 1959

Let g be a complex simple Lie algebra and let G be the adjoint group of g. It is by now classical that the Poincare polynomial p G (t) of G factors into the form

### Simple groups of Lie type

- Mathematics
- 1972

Partial table of contents: The Classical Simple Groups. Weyl Groups. Simple Lie Algebras. The Chevalley Groups. Unipotent Subgroups. The Diagonal and Monomial Subgroups. The Bruhat Decomposition.…

### Harmonic Analysis on Semi-Simple Lie Groups II

- Mathematics
- 1972

6 Spherical Functions - The General Theory.- 6.1 Fundamentals.- 6.1.1 Spherical Functions - Functional Properties.- 6.1.2 Spherical Functions - Differential Properties.- 6.2 Examples.- 6.2.1…