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Abstract
We classify and explicitly construct the irreducible graded representations of antispherical Hecke categories which are concentrated one degree. Each of these homogeneous representations is onedimensional and can be cohomologically constructed via a BGG resolution involving every (infinite dimensional) standard representation of the category. We hence determine the complete first row of the inverse parabolic pKazhdan–Lusztig matrix for an arbitrary Coxeter group and an arbitrary parabolic subgroup. This generalises the Weyl–Kac character formula to all Coxeter systems (and their parabolics) and proves that this generalised formula is rigid with respect to base change to fields of arbitrary characteristic.
Original language  English 

Number of pages  26 
Journal  Mathematische Zeitschrift 
DOIs  
Publication status  Published  23 Sept 2022 
Bibliographical note
Funding Information:We would like to thank George Lusztig and Stephen Donkin for their helpful comments. We would also like to thank the anonymous referees for their detailed reading of the paper and their helpful suggestions. The authors are grateful for funding from EPSRC grant EP/V00090X/1, the Royal Commission for the Exhibition of 1851, and European Research Council grant No. 677147, respectively.
Publisher Copyright:
© 2022, The Author(s).
Keywords
 Hecke categories
 pKazhdanLusztig polynomials
 WeylKac character formula
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 1 Active

Tensor and wreath products of symmetric groups
4/05/21 → 3/05/26
Project: Research project (funded) › Research