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 Ŝ
_{0}(n, r) and we conjecture that these two algebras are isomorphic when r < n. This conjecture will give a monomial basis in Ŝ
_{0}(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 |
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Original language | English |
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Awarding Institution | |
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Sponsors | ESF and EPSRC |
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Supervisor | Xiuping Su (Supervisor) & Alastair King (Supervisor) |
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- representation theory
- algebraic geometry
- quiver representations
- Projective geometry
- associativity
Affine 0-Schur algebras and affine double flag varieties
Crawley, T. (Author). 26 May 2021
Student thesis: Doctoral Thesis › PhD