Calibrated representations of affine Hecke algebras

Details Calibrated representations of affine Hecke algebras Calibrated representations of affine Hecke algebras

2004-01-23

arxiv.org/abs/math/0401323v2

These results have been extended and published in Affine Hecke algebras and generalized standard Young tableaux, J. Algebra, 2

Mathematics

Representation Theory

Scientific paper

This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated representations are indexed by placed skew shapes, (2) the dimension of an irreducible calibrated representation is the number of standard Young tableaux corresponding to the placed skew shape and (3) each irreducible calibrated representation is constructed explicitly by formulas which describe the action of each generator of the affine Hecke algebra on a specific basis in the representation space. This construction is a generalization of A. Young's seminormal construction of the irreducible representations of the symmetric group. In this sense Young's construction has been generalized to arbitrary Lie type.

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