# 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) Q Science > QA Mathematics School of Mathematics, Computer Science & Engineering > Mathematics Author 24 Oct 2019 08:46 https://openaccess.city.ac.uk/id/eprint/23029
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