On dimensions of RoCK blocks of cyclotomic quiver Hecke superalgebras
Alexander Kleshchev
TL;DR
This paper calculates the dimensions of specific blocks in cyclotomic quiver Hecke superalgebras, linking algebraic structures to representations of twisted affine Kac-Moody Lie algebras.
Contribution
It provides explicit dimension formulas for RoCK blocks of cyclotomic quiver Hecke superalgebras, connecting algebraic and Lie-theoretic computations.
Findings
Explicit dimension formulas for RoCK blocks.
Connection between algebraic blocks and Kac-Moody representations.
Computation of Shapovalov form values on explicit vectors.
Abstract
We explicitly compute the dimensions of certain idempotent truncations of RoCK blocks of cyclotomic quiver Hecke superalgebras. Equivalently, this amounts to a computation of the value of the Shapovalov form on certain explicit vectors in the basic representations of twisted affine Kac-Moody Lie algebras of type .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics