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Indecomposable tilting modules for the blob algebra

Hazi, A., Martin, P. and 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 Mathematics, Computer Science & Engineering > Mathematics
Related URLs:
URI: https://openaccess.city.ac.uk/id/eprint/23029
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