Journal of Lie Theory

no. 4
Exponential Hilbert Series and Geometric Invariants of Flag Varieties
Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 1141-1152
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.
DOI: 10.5802/jolt.1215
Classification: 17B10
Keywords: Hilbert series, Stirling numbers, algebraic groups, representation theory 
@article{JOLT_2021_31_4_a15,
     author = {W. 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},
     doi = {10.5802/jolt.1215},
     zbl = {1485.14094},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1215/}
}
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%J Journal of Lie Theory
%D 2021
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W. A. Johnson. Exponential Hilbert Series and Geometric Invariants of Flag Varieties. Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 1141-1152. doi: 10.5802/jolt.1215

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