Author:
Bowman Chris,Hazi Amit,Norton Emily
Abstract
AbstractWe classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated one degree. Each of these homogeneous representations is one-dimensional 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 p-Kazhdan–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.
Publisher
Springer Science and Business Media LLC
Reference47 articles.
1. Andersen, H. H., Jantzen, J. C., Soergel, W.: Representations of quantum groups at a $$p$$th root of unity and of semisimple groups in characteristic $$p$$: independence of $$p$$, Astérisque, no. 220, 321 (1994)
2. Achar, P., Makisumi, S., Riche, S., Williamson, G.: Koszul duality for Kac-Moody groups and characters of tilting modules. J. Am. Math. Soc. 32(1), 261–310 (2019)
3. Arakawa, T.: A new proof of the Kac-Kazhdan conjecture. Int. Math. Res. Not. Art. ID 27091, 5 (2006)
4. Arakawa, T.: Representation theory of$$\mathscr {W}$$-algebras, Invent. Math. 169(2), 219–320 (2007)
5. Berkesch Zamaere, C., Griffeth, S., Sam, S. V.: Jack polynomials as fractional quantum Hall states and the Betti numbers of the$$(k+1)$$-equals ideal, Comm. Math. Phys. 330 (2014), no. 1, 415–434. MR 3215587
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2 articles.
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