Hecke modules based on involutions in extended Weyl groups
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Let X be the group of weights of a maximal torus of a simply connected semisimple group over C and let W be the Weyl group. The semidirect product W((Q ⊗ X)/X) is called an extended Weyl group. There is a natural C(v)-algebra H called the extended Hecke algebra with basis indexed by the extended Weyl group which contains the usual Hecke algebra as a subalgebra. We construct an H-module with basis indexed by the involutions in the extended Weyl group. This generalizes a construction of the author and Vogan.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
American Mathematical Society (AMS)
Lusztig, G. "Hecke modules based on involutions in extended Weyl groups." Representation Theory 22 (December 2018): 246-277 © 2018 American Mathematical Society
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