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

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 نشر من قبل Ian Whitehead
 تاريخ النشر 2018
  مجال البحث
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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 $m_lambda in mathbb{Z}[t]$ indexed by positive imaginary roots $lambda$. At $t=0$ these polynomials evaluate to the root multiplicities, so we consider $m_lambda$ to be a $t$-deformation of $mathrm{mult} (lambda)$. We generalize the Peterson algorithm and the Berman-Moody formula for root multiplicities to compute $m_lambda$. As a consequence we deduce fundamental properties of $m_lambda$.



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