Correction factors for Kac-Moody groups and t-deformed root multiplicities

2018/06/13 by Muthiah, Dinakar, Puskás, Anna, Whitehead, Ian
#17B22 #17B67 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1806.05209

Abstract

We study a correction factor for Kac-Moody root systems which arises in the theory of p-adic Kac-Moody groups. In affine type, this factor is known, and its explicit computation is the content of the Macdonald constant term conjecture. The data of the correction factor can be encoded as a collection of polynomials m_λ∈ ℤ[t] indexed by positive imaginary roots λ. At t=0 these polynomials evaluate to the root multiplicities, so we consider m_λ to be a t-deformation of mult (λ). We generalize the Peterson algorithm and the Berman-Moody formula for root multiplicities to compute m_λ. As a consequence we deduce fundamental properties of m_λ.

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