p-Jones-Wenzl idempotents

2019/02/01 by Burrull, Gaston, Libedinsky, Nicolas, Sentinelli, Paolo · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1902.00305

Abstract

For a prime number p and any natural number n we introduce, by giving an explicit recursive formula, the p-Jones-Wenzl projector ^pJW_n, an element of the Temperley-Lieb algebra TL_n(2) with coefficients in \mathbb F_p. We prove that these projectors give the indecomposable objects in the A₁-Hecke category over \mathbb F_p, or equivalently, they give the projector in End_SL₂(\mathbb F_p)((\mathbb F_p²)^{⊗ n}) to the top tilting module. The way in which we find these projectors is by categorifying the fractal appearing in the expression of the p-canonical basis in terms of the Kazhdan-Lusztig basis for A₁.

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• Steinberg skein identities at roots of unity
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