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Titlebook: Representations of Reductive Groups; In Honor of the 60th Monica Nevins,Peter E. Trapa Book 2015 Springer International Publishing Switzerl

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,Hecke algebras with unequal parameters and Vogan’s left cell invariants, to an invariant of left cells in the sense of Kazhdan and Lusztig. Although it is not a complete invariant, it is extremely useful in describing left cells. Here, we propose a general framework for defining such invariants which also applies to Hecke algebras with unequal parameters.
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The smooth loci of spiral Schubert varieties of type ,, by the number of torus-invariant curves passing through that point. In this paper we determine the locus of smooth points of a spiral Schubert variety of type .. This continues the study begun in [7], where the locus of rationally smooth points was determined. The main result describes the smooth l
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Dirac cohomology, elliptic representations and endoscopy,hip of Dirac cohomology with .-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 8–13) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for furthe
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Comparing and characterizing some constructions of canonical bases from Coxeter systems,ntilinear map. Together, these form an example of what Webster calls a pre-canonical structure, relative to which the well-known Kazhdan–Lusztig basis of . is a canonical basis. Lusztig and Vogan defined a representation of a modified Iwahori–Hecke algebra on the free .-module generated by the set o
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