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Communications in Algebra Volume 39, 2011 - Issue 12
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Original Articles

Computing of the Combinatorial Rank of uq(š”°š”¬2n+1)

V. K. Kharchenko FES-CuautitlĆ”n, Universidad Nacional AutĆ³noma de MĆ©xico; Sobolev Institute of Mathematics, Novosibirsk 630090, RussiaCorrespondence[email protected]
&
M. L. Diaz Sosa FES-CuautitlĆ”n, Universidad Nacional AutĆ³noma de MĆ©xico; Sobolev Institute of Mathematics, Novosibirsk 630090, Russia
Pages 4705-4718 | Received 24 Oct 2010, Published online: 14 Dec 2011
 
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Abstract

The combinatorial rank of the multiparameter version of the Lusztig small quantum group u q (š”°š”¬2n+1) (the so called Frobeniusā€“Lusztig kernel of type B n ) equals āŒŠlog 2(n āˆ’ 1)āŒ‹ +2 provided that q has a finite multiplicative order t > 4.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENTS

The authors were supported by PACIVE of the FES-CuautitlƔn UNAM, project GC-19. The first author was supported by FAPESP (Brazil), grant 2010/51952-3, responsible professor I.P. Shestakov, Institute of Mathematics and Statistics of the University of Sao Paulo, Brazil.

Notes

1Here āŒŠaāŒ‹ is the biggest integer less than or equal to a. In [Citation5], confusingly the symbol āŒˆ a āŒ‰ is used instead.

Communicated by L. Rowen.

To our beautiful Miriam Cohen.

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