Journal of Lie Theory

no. 1
Notes on Harish-Chandra Cells of (sp(2n, C), GL(n, C))-Modules
Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 189-220
We fix (G,K) = (Sp(2n, C), GL(n, C))). Cells of Harish-Chandra modules partition the set of irreducible Harish-Chandra modules having the same infinitesimal character as the trivial representation. Irreducible modules in a cell form a basis of a representation of the complex Weyl group. These representations are the Harish-Chandra cells representations. The point of these notes is two-fold. We give closed formulae for the number of isomorphic cell representations. In Section 5 we give a parametrization of Harish-Chandra cells. We use our results to compute the number of Unipotent representations attached to even nilpotent orbits.
DOI: 10.5802/jolt.1165
Classification: 22E47
Keywords: Coherent continuation, Lusztig left cells 
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     author = {L. Barchini},
     title = {Notes on {Harish-Chandra} {Cells} of (sp(2n, {C),} {GL(n,} {C))-Modules}},
     journal = {Journal of Lie Theory},
     pages = {189--220},
     year = {2021},
     volume = {31},
     number = {1},
     doi = {10.5802/jolt.1165},
     zbl = {1475.22021},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1165/}
}
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L. Barchini. Notes on Harish-Chandra Cells of (sp(2n, C), GL(n, C))-Modules. Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 189-220. doi: 10.5802/jolt.1165

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