Branching Schubert calculus and the Belkale-Kumar product on cohomology

Authors:
Nicolas Ressayre and Edward Richmond

Journal:
Proc. Amer. Math. Soc. **139** (2011), 835-848

MSC (2010):
Primary 14M15, 14N15; Secondary 57T15

DOI:
https://doi.org/10.1090/S0002-9939-2010-10681-0

Published electronically:
October 1, 2010

MathSciNet review:
2745636

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Abstract | References | Similar Articles | Additional Information

Abstract: In 2006 Belkale and Kumar defined a new product on the cohomology of flag varieties and used this new product to give an improved solution to the eigencone problem for complex reductive groups. In this paper, we give a generalization of the Belkale-Kumar product to the branching Schubert calculus setting. The study of branching Schubert calculus attempts to understand the induced map on cohomology of an equivariant embedding of flag varieties. The main application of our work is a compact formulation of the solution to the branching eigencone problem.

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Additional Information

**Nicolas Ressayre**

Affiliation:
Département de Mathématiques, Université Montpellier II, Case courrier 051-Place Eugène Bataillon, 34095 Montpellier Cedex 5, France

Email:
ressayre@math.univ-montp2.fr

**Edward Richmond**

Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97402

Address at time of publication:
Department of Mathematics, University of British Columbia, Vancouver, BC, V6T172, Canada

Email:
erichmo2@uoregon.edu, erichmond@math.ubc.ca

DOI:
https://doi.org/10.1090/S0002-9939-2010-10681-0

Keywords:
Schubert calculus,
Belkale-Kumar product,
eigencone,
structure constants

Received by editor(s):
September 16, 2009

Received by editor(s) in revised form:
February 27, 2010, and April 9, 2010

Published electronically:
October 1, 2010

Additional Notes:
The first author was partially supported by the French National Research Agency (ANR-09-JCJC-0102-01).

Communicated by:
Ted Chinburg

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.