Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties
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- by A. N. Kirillov and T. Maeno
- St. Petersburg Math. J. 22 (2011), 447-462
- DOI: https://doi.org/10.1090/S1061-0022-2011-01151-3
- Published electronically: March 18, 2011
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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.References
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Bibliographic 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
- Received by editor(s): January 15, 2010
- Published electronically: March 18, 2011
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 447-462
- MSC (2010): Primary 05E15, 14M15
- DOI: https://doi.org/10.1090/S1061-0022-2011-01151-3
- MathSciNet review: 2729944
Dedicated: To Ludwig Dmitrievich Faddeev on the occasion of his 75th birthday