皆様
以下の要領にて、大阪公立大学 理学国際教育研究センターの研究セミナーが開催されます。
タイトル: Shifted quantum affine algebras and cluster algebras
日時: 11月8日（木）16:45～17:45
会場: 理学部E棟 4階 E408
アブストラクト:
This is a report on a joint work with Christof Geiss and David Hernandez (arXiv:2401.04616). Shifted quantum affine algebras have been introduced by Finkelberg and Tsymbaliuk in their study of quantized K-theoretic Coulomb branches of certain quiver gauge theories. Their representation theory has been studied by Hernandez, who constructed a category O containing finite-dimensional and infinite-dimensional representations. We introduce a new class of infinite rank cluster algebras associated with A-D-E root systems, and show that suitable completions of these cluster algebras are isomorphic to the Grothendieck rings of the category O of the corresponding shifted quantum affine algebras. In this isomorphism, the cluster variables of the initial seed are mapped to certain Q-variables and the most interesting first step mutations are instances of the QQ-system relations studied recently by Frenkel and Hernandez (arXiv:2312.13256). We conjecture that the images of all cluster monomials are classes of simple objects of O. We prove the conjecture in type A_1. We also show that it holds for the subcategory C of O whose objects are the finite-dimensional representations.
Zoomリンク:
https://omu-ac-jp.zoom.us/j/95574428004?pwd=5Ipu0bO5VqouFxIPhZ9JjurPHalnZy.1
ミーティングID: 955 7442 8004
パスコード: 959143
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