Related papers: The convolution algebra structure on $K^G(\mathcal…

For the algebraic group $SL_{l+1}(\mathbb{C})$ we describe a system of positive roots associated to conjugacy classes in its Weyl group. Using this we explicitly describe the algebra of regular functions on certain transverse slices to…

This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…

For an arbitrary finite monoid $M$ and subgroup $K$ of the unit group of $M$, we prove that there is a bijection between irreducible representations of $M$ with nontrivial $K$-fixed space and irreducible representations of $\mathcal{H}_K$,…

We present an independent short proof of the main result of arXiv:0706.3725 that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with…

If $G$ is a finite group, the Grothendieck group ${\mathbf{K}}\_G(G)$ of the category of $G$-equivariant ${\mathbb{C}}$-vector bundles on $G$ (for the action of $G$ on itself by conjugation) is endowed with a structure of (commutative)…

We construct a new quantization $K_t(\mathcal{O}^{sh}_{\mathbb{Z}})$ of the Grothendieck ring of the category $\mathcal{O}^{sh}_{\mathbb{Z}}$ of representations of shifted quantum affine algebras (of simply-laced type). We establish that…

We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given…

We briefly summarize our systematic construction procedure of q-deforming maps for Lie group covariant Weyl or Clifford algebras.

We first prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group. An essential step consists to deform the K-theoretic Hall algebra so that the…

For an $(\epsilon,G)$-color-commutative associative algebra $A$ with an identity element over a field $F$ of characteristic not 2, and for a color-commutative subalgebra $D$ of color-derivations of $A$, denote by $A[D]$ the associative…

For any Lie groupoid $G$, the vector bundle $g^*$ dual to the associated Lie algebroid $g$ is canonically a Poisson manifold. The (reduced) C*-algebra of $G$ (as defined by A. Connes) is shown to be a strict quantization (in the sense of M.…

Let G denote a group and let W be an algebra over a commutative ring R. We will say that W is a G-graded twisted algebra (not necessarily commutative, neither associative) if there exists a G-grading W=\bigoplus_{g \in G}W_{g} where each…

Bell and Zhang have shown that if $A$ and $B$ are two connected graded algebras finitely generated in degree one that are isomorphic as ungraded algebras, then they are isomorphic as graded algebras. We exploit this result to solve the…

It is known that the semi-infinite cohomology spaces of the infinitely twisted nilpotent subalgebra in an affine Lie algebra $g$ with coefficients in an integrable simple module over the affine Lie algebra have a base enumerated by elements…

We compute the based rings of two-sided cells corresponding to the unipotent class in $Sp_6(\mathbb C)$ with Jordan blocks (2211). The results also verify Lusztig's conjecture on the structure of the based rings of the two-sided cells of an…

Subalgebras of upper triangular matrix algebras have played a fundamental role in the classification of minimal varieties of polynomial growth. Such classification has become a source of study in recent years since it leads to the more…

We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group of type D (the demihyperoctahedral group, or the group of…

We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…

We investigate in detail relationships between the set ${\mathfrak B}^\infty$ of all infinite ``biconvex'' sets in the positive root system $\Delta_+$ of an arbitrary untwisted affine Lie algebra ${\mathfrak g}$ and the set ${\mathcal…

The negative part $U^-$ of a quantised enveloping algebra associated to a simple Lie algebra possesses a canonical basis $\mathcal{B}$ with favourable properties. Lusztig has associated a cone to a reduced expression $\mathbf{i}$ for the…