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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Combinatorial $B_{n}$-analogues
of Schubert polynomials


Authors: Sergey Fomin and Anatol N. Kirillov
Journal: Trans. Amer. Math. Soc. 348 (1996), 3591-3620
MSC (1991): Primary 05E15; Secondary 05E05, 14M15
MathSciNet review: 1340174
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Abstract | References | Similar Articles | Additional Information

Abstract: Combinatorial $B_{n}$-analogues of Schubert polynomials and corresponding symmetric functions are constructed and studied. The development is based on an exponential solution of the type $B$ Yang-Baxter equation that involves the nilCoxeter algebra of the hyperoctahedral group.


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Additional Information

Sergey Fomin
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
Email: fomin@math.mit.edu

Anatol N. Kirillov
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan
Email: kirillov@ker.c.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01558-9
PII: S 0002-9947(96)01558-9
Keywords: Yang-Baxter equation, Schubert polynomials, symmetric functions
Received by editor(s): January 6, 1994
Additional Notes: Partially supported by the NSF (DMS-9400914).
Article copyright: © Copyright 1996 American Mathematical Society