相关论文: Incidence Hilbert schemes and infinite dimensional…
Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a…
We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal…
When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebra plays the role of the coordinate ring of the resulting…
We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms,…
A W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. This paper concentrates on the study of 1-dimensional representations of these algebras. Under some conditions on a nilpotent element…
We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification…
The multiplicity of a weight in a finite-dimensional irreducible representation of a simple Lie algebra g can be computed via Kostant's weight multiplicity formula. This formula consists of an alternating sum over the Weyl group (a finite…
With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian…
Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…
We consider a product of three copies of infinite symmetric group and its representations spherical with respect to the diagonal subgroup. We show that such representations generate functors from a certain category of simplicial…
We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…
For W a finite (2-)reflection group and B its (generalized) braid group, we determine the Zariski closure of the image of B inside the corresponding Iwahori-Hecke algebra. The Lie algebra of this closure is reductive and generated in the…
A class of highest weight irreducible representations of the algebra $U_h(A_\infty)$, the quantum analogue of the completion and central extension $A_\infty$ of the Lie algebra $gl_\infty$, is constructed. It is considerably larger than the…
The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of…
Given a finite group $G$ and a subgroup $K$, we study the commutant of $\text{Ind}_K^G\theta$, where $\theta$ is an irreducible $K$-representation. After a careful analysis of Frobenius reciprocity, we are able to introduce an orthogonal…
A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_\Lambda$ and the inverse system algebra $R/I_\Delta$. We give a…
We prove that the direct sum of all homology groups of the integral general linear groups with Steinberg module coefficients form a commutative Hopf algebra, in particular a free graded commutative algebra. We use this to construct new…
We introduce and begin to study Lie theoretical analogs of symplectic reflection algebras for a finite cyclic group, which we call "cyclic double affine Lie algebra". We focus on type A : in the finite (resp. affine, double affine) case, we…
In this paper we construct the action of Ding-Iohara and shuffle algebras in the sum of localized equivariant K-groups of Hilbert schemes of points on C^2. We show that commutative elements K_i of shuffle algebra act through vertex…
In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g.…