相关论文: Presenting Schur Algebras

We prove that the q-Schur algebras of finite type introduced in [LW22] are cellular in the sense of Graham and Lehrer, which is a generalization of Geck's theorem on the cellularity of Hecke algebras of finite type. Moreover, we study…

We use the Hecke algebras of affine symmetric groups and their associated Schur algebras to construct a new algebra through a basis, and a set of generators and explicit multiplication formulas of basis elements by generators. We prove that…

We show that canonical bases in $\dot{U}(\mathfrak{sl}_n)$ and the Schur algebra are compatible; in fact we extend this result to $p$-canonical bases. This follows immediately from a fullness result from a functor categorifying this map. In…

In this paper we consider the (affine) Schur algebra introduced by Vign\'eras as the endomorphism algebra of certain permutation modules for the Iwahori-Matsumoto Hecke algebra. This algebra describes, for a general linear group over a…

We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra…

We introduce an analogue of the $q$-Schur algebra associated to Coxeter systems of type $\hat A_{n-1}$. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an…

We introduce an integral form U of the quantized enveloping algebra of sl_2. The algebra U is just large enough so that the quasi-R-matrix is contained in a completion of U\otimes U. We study several completions of the algebra U, and…

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 develop algebraic and geometrical approaches toward canonical bases for affine q-Schur algebras of arbitrary type introduced in this paper. A duality between an affine q-Schur algebra and a corresponding affine Hecke algebra is…

We will construct the Lusztig form for the quantum loop algebra of $\mathfrak{gl}_n$ by proving the conjecture \cite[3.8.6]{DDF} and establish partially the Schur--Weyl duality at the integral level in this case. We will also investigate…

We establish a connection between a generalization of KLR algebras, called quiver Schur algebras, and the cohomological Hall algebras of Kontsevich and Soibelman. More specifically, we realize quiver Schur algebras as algebras of…

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…

We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and…

It is known that a generalized $q$-Schur algebra may be constructed as a quotient of a quantized enveloping algebra $\UU$ or its modified form $\dot{\UU}$. On the other hand, we show here that both $\UU$ and $\dot{\UU}$ may be constructed…

We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine)…

We categorify Lusztig's version of the quantized enveloping algebra for sl(2). Using a graphical calculus a 2-category is constructed whose split Grothendieck ring is isomorphic to Lusztig's algebra. The indecomposable morphisms of this…

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 continue the development of the homological theory of quantum general linear groups previously considered by the first author. The development is used to transfer information to the representation theory of quantised Schur algebras. The…

A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…

We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras.