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2021 Fiscal Year Final Research Report

Analysis of Infinite dimensional algebras and quantum field theories and their applications

Research Project

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Project/Area Number 17K05275
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionNagoya University

Principal Investigator

Awata Hidetoshi  名古屋大学, 多元数理科学研究科, 准教授 (40314059)

Project Period (FY) 2017-04-01 – 2022-03-31
Keywordsディン・庵原・三木代数 / 量子トロイダル代数 / DAHA
Outline of Final Research Achievements

We derived the generalization of the KZ equation associated with the Ding-Iohara-Miki (DIM) algebra and its R-matrix by using the braid and shift relations of the intertwiner of the DIM algebra. We constructed the intertwiner for a MacMahon representation and show that the intertwiners are permuted using the MacMahon R-matrix. We presented a candidate for the eigenfunction of the non-stationary Dell Hamiltonian.

Free Research Field

無限次元可積分系

Academic Significance and Societal Importance of the Research Achievements

ディン・庵原・三木(DIM)代数は、ホップ代数の構造と2つの中心を持つ無限次元代数であり、W無限大代数、(q-)ビラソロ代数や(q-)W代数などをその特殊な場合とし て内包している。又、我々が発見した様に、その相関関数は5次元超対称ヤンミルズ理論のネクラソフ分配関数と一致している。そのため最近非常に注目を集めている重要な代数である。

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Published: 2023-01-30  

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