相关论文: Presentation of rational Schur algebras

We extend the family of classical Schur algebras in type A, which determine the polynomial representation theory of general linear groups over an infinite field, to a larger family, the rational Schur algebras, which determine the rational…

We give a presentation of Schur algebras (over the rational number field) by generators and relations, in fact a presentation which is compatible with Serre's presentation of the universal enveloping algebra of a simple Lie algebra. In the…

Left and right "generalized Schur algebras", previously introduced by the author, are defined and analyzed. Filtrations of these algebras lead, in most cases, to parameterizations of the their irreducible representations over fields of…

Motivated by work of R.M. Green, we obtain a presentation of Schur algebras (both the classical and quantized versions) in terms of generators and relations. The presentation is compatible with the usual presentation of the (quantized or…

We obtain a presentation of quantum Schur algebras (over the field Q(v)) by generators and relations. This presentation is compatible with the usual presentation of the quantized universal enveloping algebra of the Lie algebra gl(2). We…

We obtain a presentation of Schur algebras (and q-Schur algebras) by generators and relations which is compatible with the usual presentation of the enveloping algebra (quantized enveloping algebra) corresponding to the Lie algebra gl(n) of…

We consider the representation dimension, for fixed $n\geq2$, of ordinary and quantised Schur algebras $S(n,r)$ over a field $k$. For $k$ of positive characteristic $p$ we give a lower bound valid for all $p$. We also give an upper bound in…

We give geometric descriptions of the category C_k(n,d) of rational polynomial representations of GL_n over a field k of degree d for d less than or equal to n, the Schur functor and Schur-Weyl duality. The descriptions and proofs use a…

We define a generic multiplication in quantised Schur algebras and thus obtain a new algebra structure in the Schur algebras. We prove that via a modified version of the map from quantum groups to quantised Schur algebras, defined by A. A.…

The affine Schur algebra $\widetilde{S}(n,r)$ (of type A) over a field $K$ is defined to be the endomorphism algebra of the tensor space over the extended affine Weyl group of type $A_{r-1}$. By the affine Schur-Weyl duality it is…

We compute the equations of all rational double point singularities and we determine their types over perfect ground fields $k$ that arise as quotient singularities by finite linearly reductive subgroup schemes of $\textrm{SL}_{2,k}$.

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…

Isomorphisms are constructed between generalized Schur algebras in different degrees. The construction covers both the classical case (of general linear groups over infinite fields of arbitrary characteristic) and the quantized case (in…

One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous…

We prove that any projective Schur algebra over a field $K$ is equivalent in $Br(K)$ to a radical abelian algebra. This was conjectured in 1995 by Sonn and the first author of this paper. As a consequence we obtain a characterization of the…

We give explicit presentations by generators and relations of certain generalized Schur algebras (associated with tensor powers of the natural representation) in types B, C, D. This extends previous results in type A obtained by two of the…

We find an explicit presentation of relative linear Steinberg groups $\mathrm{St}(n, R, I)$ for any ring $R$ and $n \geq 4$ by generators and relations as abstract groups. We also prove a similar result for relative simply laced Steinberg…

Let k be an algebraically closed field of characteristic p>0, let m,r be integers with m\ge1, r\ge0 and m\ge r and let S_0(2m,r) be the symplectic Schur algebra over k as introduced by the first author. We introduce the symplectic Schur…

We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Cherednik algebras associated to the general and special…