Geodesic
Exponential Hilbert Series and Geometric Invariants of Flag Varieties
Wayne A. Johnson1
1Westminster College, Fulton, MO 65251, U.S.A.
Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1141-1152

Voir la notice de l'article provenant de la source Heldermann Verlag

We study properties of the exponential Hilbert series of a (partial) flag variety, G/P, where G is a semisimple, simply-connected complex linear algebraic group and P is a parabolic subgroup. We prove a relationship between the exponential Hilbert series and the degree and dimension of the flag variety. We then prove a combinatorial formula for the coefficients of an exponential analogue of the Hilbert polynomial. This formula is used in examples to prove further combinatorial identities involving Stirling numbers of the first and second kinds.
Classification : 17B10
Mots-clés : Hilbert series, Stirling numbers, algebraic groups, representation theory

Wayne A. Johnson  1

1 Westminster College, Fulton, MO 65251, U.S.A. 
Wayne A. Johnson. Exponential Hilbert Series and Geometric Invariants of Flag Varieties. Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1141-1152. http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a15/
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     author = {Wayne A. Johnson},
     title = {Exponential {Hilbert} {Series} and {Geometric} {Invariants} of {Flag} {Varieties}},
     journal = {Journal of Lie Theory},
     pages = {1141--1152},
     year = {2021},
     volume = {31},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a15/}
}
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