Affine 0-Schur algebras and affine double flag varieties

Student thesis: Doctoral ThesisPhD

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 Award26 May 2021
Original languageEnglish
Awarding Institution
  • University of Bath
SponsorsESF and EPSRC
SupervisorXiuping Su (Supervisor) & Alastair King (Supervisor)

Keywords

  • representation theory
  • algebraic geometry
  • quiver representations
  • Projective geometry
  • associativity

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