Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tensor product multiplicities for crystal bases of extremal weight modules over quantum infinite rank affine algebras of types $ B_{\infty}$, $ C_{\infty}$, and $ D_{\infty}$


Authors: Satoshi Naito and Daisuke Sagaki
Journal: Trans. Amer. Math. Soc. 364 (2012), 6531-6564
MSC (2010): Primary 17B37; Secondary 05E10, 05A19, 17B67
Published electronically: May 29, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Using Lakshmibai-Seshadri paths, we give a combinatorial realization of the crystal basis of an extremal weight module of a (general) integral extremal weight over the quantized universal enveloping algebra associated to the infinite rank affine Lie algebra of type $ B_{\infty }$, $ C_{\infty }$, or $ D_{\infty }$. Moreover, via this realization, we obtain an explicit description (in terms of Littlewood-Richardson coefficients) of how tensor products of these crystal bases decompose into connected components when their extremal weights are of nonnegative levels. These results in types $ B_{\infty }$, $ C_{\infty }$, and $ D_{\infty }$ extend the corresponding results due to Kwon in types $ A_{+\infty }$ and $ A_{\infty }$. Our results above also include, as a special case, the corresponding results (concerning crystal bases) due to Lecouvey in types $ B_{\infty }$, $ C_{\infty }$, and $ D_{\infty }$, where the extremal weights are of level zero.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 17B37, 05E10, 05A19, 17B67

Retrieve articles in all journals with MSC (2010): 17B37, 05E10, 05A19, 17B67


Additional Information

Satoshi Naito
Affiliation: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
Email: naito@math.titech.ac.jp

Daisuke Sagaki
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
Email: sagaki@math.tsukuba.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05597-8
PII: S 0002-9947(2012)05597-8
Received by editor(s): May 11, 2010
Received by editor(s) in revised form: December 29, 2010, and April 1, 2011
Published electronically: May 29, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.