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P-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras
He, Xuhua1; Nie, Sian2
AbstractThe cocenter of an affine Hecke algebra plays an important role in the study of representations of the affine Hecke algebra and the geometry of affine Deligne-Lusztig varieties (see for example, He and Nie in Compos Math 150(11):1903-1927, 2014; He in Ann Math 179:367-404, 2014; Ciubotaru and He in Cocenter and representations of affine Hecke algebras, 2014). In this paper, we give a Bernstein-Lusztig type presentation of the cocenter. We also obtain a comparison theorem between the class polynomials of the affine Hecke algebra and those of its parabolic subalgebras, which is an algebraic analog of the Hodge-Newton decomposition theorem for affine Deligne-Lusztig varieties. As a consequence, we present a new proof of the emptiness pattern of affine Deligne-Lusztig varieties (Gortz et al. in Compos Math 146(5):1339-1382, 2010; Gortz et al. in Ann Sci Acole Norm Sup, 2012).
KeywordAffine Hecke algebras Cocenters Parabolic subalgebras
Funding ProjectHKRGC[602011]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000357494400006
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Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.Hong Kong Univ Sci & Technol, Inst Adv Study, Dept Math, Clear Water Bay, Kowloon, Hong Kong, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
He, Xuhua,Nie, Sian. P-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras[J]. SELECTA MATHEMATICA-NEW SERIES,2015,21(3):995-1019.
APA He, Xuhua,&Nie, Sian.(2015).P-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras.SELECTA MATHEMATICA-NEW SERIES,21(3),995-1019.
MLA He, Xuhua,et al."P-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras".SELECTA MATHEMATICA-NEW SERIES 21.3(2015):995-1019.
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