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Combinatorial Representation Theory and Crystal Bases

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Proceedings of the Third International Algebra Conference

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Abstract

Let F be a field and A be an associative algebra over F. For instance, we may take A to be the group algebra F[G] of a group G or the universal enveloping algebra U(g) of a Lie algebra g. Let V be an F-vector space. By a representation of A on V, we mean an algebra homomorphism ø: A → End(V). In this case, V becomes an A-module with the A-action given by

EquationSource % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiabgw % Sixlabe27aUjabg2da9iabew9aMjaacIcacaWGHbGaaiykaiaacIca % cqaH9oGBcaGGPaacbaGaa8hiaiaa-zgacaWFVbGaa8NCaiaa-bcaca % WFHbGaa8hBaiaa-XgacaWFGaGaamyyaiabgIGiolaadgeacaGGSaGa % eqyVd4MaeyicI4SaamOvaiaac6caaaa!5315! ]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ a \cdot \nu = \phi (a)(\nu ) for all a \in A,\nu \in V. $$

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This research was supported by KOSEF Grant #98-0701-01-5-L and the Young Scientist Award, Korean Academy of Science and Technology.

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Authors and Affiliations

  1. School of Mathematics, Korea Institute for Advanced Study, Seoul, 130-012, Korea

    Seok-Jin Kang

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  1. Seok-Jin Kang
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© 2003 Springer Science+Business Media Dordrecht

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Kang, SJ. (2003). Combinatorial Representation Theory and Crystal Bases. In: Proceedings of the Third International Algebra Conference. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0337-6_4

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  • DOI: https://doi.org/10.1007/978-94-017-0337-6_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6351-9

  • Online ISBN: 978-94-017-0337-6

  • eBook Packages: Springer Book Archive

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