구독자 여러분께,

Quantum affine algebra 관련 talk 하나를 소개해 드립니다.

관심 있으신 분의 많은 참여 바랍니다.

이수홍 올림 ---------- Forwarded message ---------- From: 'Yoshiyuki Kimura' via Minami Osaka Daisu Seminar modseminar@googlegroups.com Date: Nov 7, 2024, 12:15 AM +0900 To: modseminar@googlegroups.com Subject: 大阪公立大学 理学国際教育研究センター(11/8)

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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-- Yoshiyuki Kimura Faculty of Liberal Arts, Sciences and Global Education Osaka Metropolitan University 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan Research map: http://researchmap.jp/ysykmr/ -- You received this message because you are subscribed to the Google Groups "Minami Osaka Daisu Seminar" group. To unsubscribe from this group and stop receiving emails from it, send an email to modseminar+unsubscribe@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/modseminar/9ba7a32a-a6e3-481d-a291-c84d80d....