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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties


Authors: A. N. Kirillov and T. Maeno
Original publication: Algebra i Analiz, tom 22 (2010), nomer 3.
Journal: St. Petersburg Math. J. 22 (2011), 447-462
MSC (2010): Primary 05E15, 14M15
Published electronically: March 18, 2011
MathSciNet review: 2729944
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Abstract: For a root system of type $ A$, a certain extension of the quadratic algebra invented by S. Fomin and the first author is introduced and studied, which makes it possible to construct a model for the equivariant cohomology ring of the corresponding flag variety. As an application, a generalization of the equivariant Pieri rule for double Schubert polynomials is described. For a general finite Coxeter system, an extension of the corresponding Nichols-Woronowicz algebra is constructed. In the case of finite crystallographic Coxeter systems, a construction is presented of an extended Nichols-Woronowicz algebra model for the equivariant cohomology of the corresponding flag variety.


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Additional Information

A. N. Kirillov
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
Email: kirillov@kurims.kyoto-u.ac.jp

T. Maeno
Affiliation: Department of Electrical Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
Email: maeno@kuee.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01151-3
PII: S 1061-0022(2011)01151-3
Keywords: Root system of type $A$, equivariant Pieri rule, Nichols–Woronowicz algebra
Received by editor(s): January 15, 2010
Published electronically: March 18, 2011
Dedicated: To Ludwig Dmitrievich Faddeev on the occasion of his 75th birthday
Article copyright: © Copyright 2011 American Mathematical Society