Unitary Hecke algebra modules with nonzero Dirac cohomology
Dan Barbasch, Dan Ciubotaru
TL;DR
This paper reviews the Dirac operator construction for graded affine Hecke algebras and computes the Dirac cohomology for irreducible unitary modules of the graded Hecke algebra of gl(n).
Contribution
It introduces the Dirac operator in the context of graded affine Hecke algebras and provides explicit calculations of Dirac cohomology for specific modules.
Findings
Explicit Dirac cohomology for irreducible unitary modules of graded Hecke algebra of gl(n)
Clarification of the Dirac operator's role in the representation theory of Hecke algebras
Enhanced understanding of unitary modules via Dirac cohomology
Abstract
In this paper, we review the construction of the Dirac operator for graded affine Hecke algebras and calculate the Dirac cohomology of irreducible unitary modules for the graded Hecke algebra of gl(n).
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry