Abstract
We present a survey of recent developments of the Beilinson–Lusztig–MacPherson approach in the study of quantum \({\mathfrak{g}\mathfrak{l}}_{n}\), infinitesimal quantum \({\mathfrak{g}\mathfrak{l}}_{n}\), quantum \({\mathfrak{g}\mathfrak{l}}_{\infty }\) and their associated q-Schur algebras, little q-Schur algebras and infinite q-Schur algebras. We also use the relationship between quantum \({\mathfrak{g}\mathfrak{l}}_{\infty }\) and infinite q-Schur algebras to discuss their representations.
Mathematics Subject Classifications (2000): 17B20, 17B35, 20G15
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Du, J., Fu, Q. (2010). Quantum \(\mathfrak{gl}_n,\) q-Schur Algebras and Their Infinite/Infinitesimal Counterparts. In: Gyoja, A., Nakajima, H., Shinoda, Ki., Shoji, T., Tanisaki, T. (eds) Representation Theory of Algebraic Groups and Quantum Groups. Progress in Mathematics, vol 284. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4697-4_5
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DOI: https://doi.org/10.1007/978-0-8176-4697-4_5
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