Related papers: Geometric construction of Schur algebras

We compute the Borel equivariant cohomology ring of the left $K$-action on a homogeneous space $G/H$, where $G$ is a connected Lie group, $H$ and $K$ are closed, connected subgroups and $2$ and the torsion primes of the Lie groups are units…

The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given…

We give an algebraic description of several modules and algebras related to the vector partition function, and we prove that they can be realized as the equivariant K-theory of some manifolds that have a nice combinatorial description. We…

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…

We provide a presentation of the Schur superalgebra and its quantum analogue which generalizes the work of Doty and Giaquinto for Schur algebras. Our results include a basis for these algebras and a presentation using weight idempotents in…

We obtain a presentation by generators and relations for generalized Schur algebras and their quantizations. This extends earlier results obtained in the type A case. The presentation is compatible with Lusztig's modified form of a…

We give a combinatorial expansion of a Schubert homology class in the affine Grassmannian Gr_{SL_k} into Schubert homology classes in Gr_{SL_{k+1}}. This is achieved by studying the combinatorics of a new class of partitions called…

We formulate and classify super Satake diagrams under a mild assumption, building on arbitrary Dynkin diagrams for finite-dimensional basic Lie superalgebras. We develop a theory of quantum supersymmetric pairs associated to the super…

This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext…

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

Let $A$ be a not necessarily commutative monoid with zero such that projective $A$-acts are free. This paper shows that the algebraic K-groups of $A$ can be defined using the +-construction and the Q-construction. It is shown that these two…

We develop a graded version of the theory of cyclotomic q-Schur algebras, in the spirit of the work of Brundan-Kleshchev on Hecke algebras and of Ariki on q-Schur algebras. As an application, we identify the coefficients of the canonical…

A ladder algebraic structure for $L^2(\mathbb{R}^+)$ which closes the Lie algebra $h(1)\oplus h(1)$, where $h(1)$ is the Heisenberg-Weyl algebra, is presented in terms of a basis of associated Laguerre polynomials. Using the Schwinger…

Let ${\boldsymbol{\mathfrak D}_{\vartriangle}}(n)$ be the double Ringel--Hall algebra of the cyclic quiver $\triangle(n)$ and let $\dot{\boldsymbol{\mathfrak D}_{\vartriangle}}(n)$ be the modified quantum affine algebra of…

In this paper we give a geometric construction of Cherednik's double affine Hecke algebra. We construct the algebra as the equivariant $K$-theory of the Lagrangian subvariety of the cotangent variety of the square of the flag variety of…

We define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalisation, for type B, of cyclotomic quiver Hecke algebras which are a…

We generalize the K\"unneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a corollary we obtain a universal coefficient theorem for…

Expanding the classic works of Kazhdan-Lusztig and Deodhar, we establish bar involutions and canonical (i.e., quasi-parabolic KL) bases on quasi-permutation modules over the type B Hecke algebra, where the bases are parameterized by cosets…

We provide an equivalence between the category of affine, smooth group schemes over the ring of generalized dual numbers $k[I]$, and the category of extensions of the form $1 \rightarrow \text{Lie}(G, I) \rightarrow E \rightarrow G…

We construct Kn\"orrer type equivalences outside of the hypersurface case, namely, between singularity categories of cyclic quotient surface singularities and certain finite dimensional local algebras. This generalises Kn\"orrer's…