Related papers: A generic multiplication in quantised Schur algebr…
We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types. Under the specialization of $q$ and coefficients to 1, these bases are generic bases of finite and affine cluster algebras.
This paper reveals some new analytical and geometrical properties of the generalized algebraic multiplicity, $\chi$, introduced in [7, 5] and further developed in [20, 23, 24]. In particular, it establishes a completely new connection…
We introduce a new quantized enveloping superalgebra $\mathfrak{U}_q{\mathfrak{p}}_n$ attached to the Lie superalgebra ${\mathfrak{p}}_n$ of type $P$. The superalgebra $\mathfrak{U}_q{\mathfrak{p}}_n$ is a quantization of a Lie…
By embedding the Hecke algebra $\check H_q$ of type $D$ into the Hecke algebra $H_{q,1}$ of type $B$ with unequal parameters $(q,1)$, the $q$-Schur algebras $S^\kappa_q(n,r)$ of type $D$ is naturally defined as the endomorphism algebra of…
It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
Similar to works of G. Ellis (1998), the concept of covering pair of Lie algebras is defined. Also, we show the existence of covering pair for the pair of Lie algebras (L,N) and then show that every crossed module is a homomorphic image of…
We consider the Kronecker quiver and determine the relations for the specialisation to q=0 of the generic composition algebra as well as those for Reineke's composition monoid. We also obtain a normal form for the varieties occurring in the…
We show that the defining relations needed to describe a generalized q-Schur algebra as a quotient of a quantized enveloping algebra are determined completely by the defining ideal of a certain finite affine variety, the points of which…
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…
A geometric construction of Lusztig's modified quantum algebra of symmetric type is presented by using certain localized equivariant derived categories of double framed representation varieties of quivers.
A subset P of N x N is called Schur bounded if every infinite matrix with bounded entries which is zero off of P yields a bounded Schur multiplier on B(H). Such sets are characterized as being the union of a subset with at most k entries in…
This is a generalization of the classic work of Beilinson, Lusztig and MacPherson. In this paper (and an Appendix) we show that the quantum algebras obtained via a BLM-type stabilization procedure in the setting of partial flag varieties of…
Extending the corresponding notion for matrices or bounded linear operators on a Hilbert space we define a generalized Schur complement for a non-negative linear operator mapping a linear space into its dual and derive some of its…
To a tree of semi-simple algebras we associate a qurve (or formally smooth algebra) S. We introduce a Zariski- and etale quiver describing the finite dimensional representations of S. In particular, we show that all quotient varieties of…
We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for q-Schur superalgebras. This gives a combinatorialisation of the relative norm approach developed by the…
In this paper the authors investigate the $q$-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type A. The authors present a coordinate algebra type construction that allows us to…
We explore some aspects of the generalized Schur limit, defined in arXiv:2506.13764. Based on several examples, we conjecture that the generalized Schur limit as a function of $\alpha$ solves a modular linear differential equation of fixed…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
The symmetric Grothendieck polynomials generalize Schur polynomials and are Schur-positive by degree. Combinatorially this is manifested as the generalization of semistandard Young tableaux by set-valued tableaux. We define a (weak)…