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• W3111036353 abstract "In these lecture notes for a summer mini-course, we provide an exposition on quantum groups and Hecke algebras, including (quasi) R-matrix, canonical basis, and $q$-Schur duality. Then we formulate their counterparts in the setting of $imath$quantum groups arising from quantum symmetric pairs, including (quasi) K-matrix, $imath$-canonical basis, and $imath$Schur duality. As an application, the ($imath$-)canonical bases are used to formulate Kazhdan-Lusztig theories and character formulas in the BGG categories for Lie (super)algebras of type A-D. Finally, geometric constructions for $q$-Schur and $imath$Schur dualities are provided." @default.
• W3111036353 created "2020-12-21" @default.
• W3111036353 creator A5048829094 @default.
• W3111036353 creator A5059827958 @default.
• W3111036353 date "2020-12-13" @default.
• W3111036353 modified "2023-09-27" @default.
• W3111036353 title "Lectures on dualities ABC in representation theory" @default.
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• W3111036353 doi "https://doi.org/10.48550/arxiv.2012.07203" @default.
• W3111036353 hasPublicationYear "2020" @default.
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