We produce an explicit recursive formula which computes the idempotent projecting to any indecomposable Soergel bimodule for a universal Coxeter system. This gives the exact set of primes for which the positive characteristic analogue of Soergel’s conjecture holds. Along the way, we introduce the multicolored Temperley-Lieb algebra.
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Elias et al. (2016) studied this question.
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