Document Type
Article
Publication Date
11-21-2019
Published In
Mathematische Zeitschrift
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 mλ∈Z[t] indexed by positive imaginary roots λ. At t=0 these polynomials evaluate to the root multiplicities, so we consider mλ to be a t-deformation of mult(λ). We generalize the Peterson algorithm and the Berman–Moody formula for root multiplicities to compute mλ. As a consequence we deduce fundamental properties of mλ.
Recommended Citation
D. Muthiah, A. Puskás, and Ian Whitehead.
(2019).
"Correction Factors For Kac–Moody Groups And t-Deformed Root Multiplicities".
Mathematische Zeitschrift.
DOI: 10.1007/s00209-019-02419-1
https://works.swarthmore.edu/fac-math-stat/256
Comments
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