Affine 0-Schur algebras and affine double flag varieties

Abstract

Affine q-Schur algebras admit a geometric construction as a convolution algebra on the set of functions with constructible support on double affine flag varieties, due to Ginzburg and Vasserot [17], Varagnolo and Vasserot [36] and Lusztig [28]. Using the geometry of affine flag varieties we define a generic product of orbits in the double flag varieties which leads to the construction of a new associative Z-algebra Ĝ(n, r), called the generic affine algebra. We then study the link between Ĝ(n, r) and the affine 0-Schur algebra Ŝ₀(n, r) and we conjecture that these two algebras are isomorphic when r < n. This conjecture will give a monomial basis in Ŝ₀(n, r) and a presentation by a quiver with relations. This work generalises the work of Jensen and Su [25] in the type A case, which gives a geometric realisation of 0-Schur algebras.

Date of Award	26 May 2021
Original language	English
Awarding Institution	University of Bath
Sponsors	ESF and EPSRC
Supervisor	Xiuping Su (Supervisor) & Alastair King (Supervisor)