Related papers: On the continuous series for affine sl(2,R)

We show how to construct unitary dual $2$-cocycles for a class of semidirect products that exhibit many similarities with the affine group ${\rm Aff}(V)=\GL(V)\ltimes V$ of a finite dimensional vector space over a local skew field. The…

To follow up on the results of [1], we propose a computationally efficient explicit cyclic decomposition of the maximal tori in the groups $SL_n(q)$ and $SU_n(q)$ and their projective images. We also derive some corollaries to simplify…

In this paper, we point out connections between certain types of indecomposable representations of $sl(2)$ and generalizations of well-known orthogonal polynomials. Those representations take the form of infinite dimensional chains of…

In this note we illustrate by a few examples the general principle: interesting algebras and representations defined over Z_+ come from category theory, and are best understood when their categorical origination has been discovered. We show…

In this article, we develop a generalization of finitary birepresentation theory applicable to Soergel bimodules for infinite Coxeter groups. We establish a reduction process for the classification of simple birepresentations of almost…

This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated…

In this note we explain, in terms of finite dimensional representations of Lie algebras $\mathfrak{sp}_{2\ell}\subset\mathfrak{sl}_{2\ell}$, a combinatorial coincidence of difference conditions in two constructions of combinatorial bases…

Let $K/F$ be a quadratic extension of $p$-adic fields, and $n$ a positive integer. A smooth irreducible representation of the group $GL(n,K)$ is said to be distinguished, if it admits on its space a nonzero $GL(n,F)$-invariant linear form.…

This is a follow-up to the paper in which we categorified the affine quantum Schur algebra S(n,r) for 2 < r < n, using a quotient of Khovanov and Lauda's categorification of the affine quantum sl_n. In this paper we categorify S(n,n) for n…

In this paper, we consider certain descending filtrations of the $\mathrm{SL}(m,\C)$-representation algebras of free groups and free abelian groups. By using it, we introduce analogs of the Johnson homomorphisms of the automorphism groups…

Two Lie algebroids are presented that are linked to the construction of the linearizing output of an affine in the input nonlinear system. The algorithmic construction of the linearizing output proceeds inductively, and each stage has two…

We study the finite-dimensional continuous complex representations of $\mathrm{SL}_2$ over the ring of integers of non-Archimedean local fields of even residual characteristic. We prove that for characteristic two, the abscissa of…

Let $V$ be a finite dimensional representations of the group $\operatorname{SL}_2$ of $2\times 2$ matrices with complex coefficients and determinant one. Let $R=\mathbb{C}[V]^{\operatorname{SL}_2}$ be the algebra of…

In this paper we prove that the affine Schur algebra $\s$ is affine cellular over $\bbq$. As an application, we prove it is of finite global dimension.

In this article, we study the modular representations of the special linear group of degree two over a finite field in defining characteristic. In particular, we study the automorphisms of derived category of representations. We have been…

We construct a model for the tensor product of the regular 2-representation of the enveloping algebra of $\mathfrak{sl}_2^+$ with the vector 2-representation, based on the $\infty$-categorical definition of the second author. Our model…

Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…

We construct an explicit abelian model for the operation of tensor $2$-product of $2$-representations of $\mathfrak{sl}_{2}^{+}$, specifically the product of a simple $2$-representation $\mathcal{L}(1)$ with a given abelian…

There exist two different languages, the ^sl(2) and N=2 ones, to describe similar structures; a dictionary is given translating the key representation-theoretic terms related to the two algebras. The main tool to describe the structure of…

In this paper, using a quantum superalgebra associated with the universal central extension of sl(2,2)^{(1)}, we introduce new R-matrices having an extra parameter x. As x\to 0, they become those associated with the symmetric and…