第5回

日時

2024年11月14日(木) 17:30~19:00

場所

i-Siteなんば S1 (およびZoomのハイブリッド形式の予定)

講演者

Davide Dal Martello氏(立教大学)

タイトル

From PVI to GDAHA via quantum middle convolution

アブストラクト

The Painlevé VI equation governs the isomonodromic deformation problem of selected 2-dimensional Fuchsian and 3-dimensional Birkhoff linear systems, the two identified by Harnad duality. Fuchsian monodromy data are known to quantize as the $C^\vee C_1$ DAHA. By factoring over the middle convolution, we obtain a formulation for duality admitting a natural monodromic translation, which turns quantum in the noncommutative sense. The resulting machinery, involving a quantum multiplicative middle convolution, allows to quantize the Birkhoff Stokes data inside the family of generalized double affine Heck algebras (GDAHA). In particular, the Birkhoff analogue to the DAHA is a specialization of the $\tilde{E}_6$-type GDAHA.

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