Related papers: Kostant's generating functions and McKay-Slodowy c…

A fundamental result in representation theory is Kostant's theorem which describes the algebra of polynomials on a reductive Lie algebra as a module over its invariants. We prove a quantum analogue of this theorem for the general linear…

The construction of integrity bases for invariant and covariant polynomials built from aset of three dimensional vectors under the SO(3) and O(3) symmetries is presented. Thispaper is a follow--up to our previous work that dealt with a set…

We derive two multivariate generating functions for three-dimensional Young diagrams (also called plane partitions). The variables correspond to a colouring of the boxes according to a finite Abelian subgroup G of SO(3). We use the vertex…

For a countable group $G$ we construct a small, idempotent complete, symmetric monoidal, stable $\infty$-category $\mathrm{KK}^{G}_{\mathrm{sep}}$ whose homotopy category recovers the triangulated equivariant Kasparov category of separable…

We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from Quantum Gravity. Specifically we consider a two-parameter class of twisted Poincar\'e algebras, from which Lie-algebraic…

Kac-Moody groups $G$ over $\mathbb{R}$ have been conjectured to occur as symmetry groups of supergravities in dimensions less than 3, and their integer forms $G(\mathbb{Z})$ are conjecturally U-duality groups. Mathematical descriptions of…

Every symmetric generating functional of a convolution semigroup of states on a locally compact quantum group is shown to admit a dense unital $*$-subalgebra with core-like properties in its domain. On the other hand we prove that every…

We study the Poincare polynomials of isotypic components of a natural family of graded GL(n)-modules supported in the closure of a nilpotent conjugacy class. These polynomials generalize the Kostka-Foulkes and are q-analogues of…

Let T be an involution of the finite dimensional complex reductive Lie algebra g and g=k+p be the associated Cartan decomposition. Denote by K the adjoint group of k. The K-module p is the union of the subsets p^{(m)}={x | dim K.x =m},…

Representations of the non-semisimple superalgebra $gl(2|2)$ in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical…

Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $\theta$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_\theta(G) \subseteq V$ of semistable points. We give necessary,…

For every involution $\mathbf{w}$ of the symmetric group $S_n$ we establish, in terms ofa special canonical quotient of the dominant Verma module associated with $\mathbf{w}$, an effective criterion, which allows us to verify whether the…

We consider the moduli space of the McKay quiver representations associated to the binary polyhedral groups G < SU(2) < SU(3). The derived category of such representations is equivalent to the derived category of coherent sheaves on the…

For the p-adic group G=SL (2) , we present results of the computations of the sums of the Bernstein projectors of a given depth. Motivation for the computations is based on a conversation with Roger Howe in August 2013. The computations are…

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6),…

We consider a generalization of Donkin-Koppinen filtrations for coordinate superalgebras of general linear supergroups. More precisely, if $G=GL(m|n)$ is a general linear supergroup of (super)degree $(m|n)$, then its coordinate superalgebra…

Let g be a semi-simple Lie algebra and let h be a reductive subalgebra of maximal rank in g. Given any irreducible representation of g, consider its tensor product with the spin representation associated to the orthogonal complement of h in…

This note extends some results of a previous paper (math.RT/0403250) about finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a…

Schuermann's theory of quantum Levy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalgebras. Quantum stochastic…

In commutative algebra, a Weitzenb\"ock derivation is a nonzero triangular linear derivation of the polynomial algebra $K[x_1,...,x_m]$ in several variables over a field $K$ of characteristic 0. The classical theorem of Weitzenb\"ock states…