2018/09/27 by Hazi, Amit, Martin, Paul, Parker, Alison
#20C08 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1809.10612
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 A1.