Journal Article

Fusion products, cohomology of GLN flag manifolds, and Kostka polynomials

Rinat Kedem

in International Mathematics Research Notices

Volume 2004, issue 25, pages 1273-1298
Published in print January 2004 | ISSN: 1073-7928
Published online January 2004 | e-ISSN: 1687-0247 | DOI:

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We explain the relation between the fusion product of symmetric power [math] evaluation modules, as defined by Feigin and Loktev, and the graded coordinate ring Rμ which describes the cohomology ring of the flag variety [math] of GLN. The graded multiplicity spaces appearing in the decomposition of the fusion product into irreducible [math]-modules are identified with the multiplicity spaces of the Specht modules in Rμ. This proves that Kostka polynomials give the character of the fusion product in this case. In the case of the product of fundamental evaluation modules, we give the precise correspondence with the reduced wedge product, and thus the usual wedge space construction of irreducible level-1 [math]-modules in the limit N → ∞. The multiplicity spaces are [math]-algebra modules in this limit.

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Subjects: Mathematics