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Canonical bases and standard monomials

Published online by Cambridge University Press:  20 January 2009

B. R. Marsh
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Abstract

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Let U be the quantized enveloping algebra associated to a simple Lie algebra g by Drinfel'd and Jimbo. Let λ be a classical fundamental weight for g, and ⋯(λ) the irreducible, finite-dimensional type 1 highest weight U-module with highest weight λ. We show that the canonical basis for ⋯(λ) (see Kashiwara [6, §0] and Lusztig [18, 14.4.12]) and the standard monomial basis (see [11, §§2.4 and 2.5]) for ⋯(λ) coincide.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 3 , October 1998 , pp. 611 - 623
Copyright
Copyright © Edinburgh Mathematical Society 1998

Footnotes

Last updated 14 April 2022

References

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