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Rectangle Diagrams for the Lusztig Cones of Quantized Enveloping Algebras of Type A

✍ Scribed by Robert Marsh

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 239 KB
Volume: 249
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9031

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✦ Synopsis

Let U be the quantum group associated to a Lie algebra g of type A n . The negative part U -of U has a canonical basis B defined by Lusztig and Kashiwara, with favorable properties. We show how the spanning vectors of the cones defined by Lusztig (1993, Israel Math. Conf. Proc. 7, 117-132), when regarded as monomials in Kashiwara's root operators, can be described using a remarkable rectangle combinatorics. We use this to calculate the Lusztig parameters of the corresponding canonical basis elements, conjecturing that translates of these vectors span the simplicial regions of linearity of Lusztig's piecewise-linear function (1990,

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