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Indecomposable tilting modules for the blob algebra

Hazi, A., Martin, P. & Parker, A. (2019). Indecomposable tilting modules for the blob algebra. City, University of London.

Abstract

The blob algebra is a finite-dimensional quotient of the Hecke algebra of type $B$ which is almost always quasi-hereditary. We construct the indecomposable tilting modules for the blob algebra over a field of characteristic $0$ in the doubly critical case. Every indecomposable tilting module of maximal highest weight is either a projective module or an extension of a simple module by a projective module. Moreover, every indecomposable tilting module is a submodule of an indecomposable tilting module of maximal highest weight. We conclude that the graded Weyl multiplicities of the indecomposable tilting modules in this case are given by inverse Kazhdan-Lusztig polynomials of type $\tilde{A}_1$.

Publication Type: Monograph (Working Paper)
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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