A polytope calculus for semisimple groups

Anderson, Jared E.

Duke Math. J., Tome 120 (2003) no. 3, p. 567-588 / Harvested from Project Euclid

Résumé

We define a collection of polytopes associated to a semisimple group $\mathsf {G}$. Weight multiplicities and tensor product multiplicities may be computed as the number of such polytopes fitting in a certain region. The polytopes are defined as moment map images of algebraic cycles discovered by I. Mirković and K. Vilonen. These cycles are a canonical basis for the intersection homology of (the closures of the strata of) the loop Grassmannian.

Publié le : 2003-03-15
Classification: 20G05, 14L99

@article{1085598302,
     author = {Anderson, Jared E.},
     title = {A polytope calculus for semisimple groups},
     journal = {Duke Math. J.},
     volume = {120},
     number = {3},
     year = {2003},
     pages = { 567-588},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1085598302}
}

Anderson, Jared E. A polytope calculus for semisimple groups. Duke Math. J., Tome 120 (2003) no. 3, pp.  567-588. http://gdmltest.u-ga.fr/item/1085598302/