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Blocks of KLR algebras of small defect

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Conference: Representations of Symmetric Groups, Hecke Algebras and KLR Algebras

We look at some (graded) decomposition numbers and adjustment matrices for blocks of KLR algebras of small defect, with particular interest in cases where the adjustment matrix is the identity matrix. We consider the combinatorics of blocks in which multipartition indexing each Specht module is a multicore and present some results (joint work with Oliver Ruff) on such blocks of weight 2 and 3. We speculate on some other blocks where we believe the adjustment matrix may be the identity matrix.

This talk is part of the Algebra seminar series.

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