This article is cited in 2 papers

The algebra of quantum bosons, theb Shubert filtration, and Lusztig bases

D. P. Zhelobenko

Peoples Friendship University of Russia

Abstract: The “Schubert filtration”, defined by means of the quantum Weyl group, is considered in Drinfel'd–Jimbo quantum algebras. A description is obtained for this filtration in terms of linear relations determined by the algebra of “quantum bosons”, and also in terms of certain projection operators. The connection between this filtration and Lusztig bases and Kashiwara crystal bases is considered.

UDC: 519.46

MSC: Primary 17B35, 17B37, 17B20; Secondary 17B67, 81R50, 81R10

Received: 15.05.1992

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1994, 43:3, 397–419

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