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Jason Fulman, Rita Jiménez Rolland, and Jennifer C. H. Wilson
Generating functions and statistics on spaces of maximal tori in classical Lie groups view print
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| Published: |
February 8, 2017 |
| Keywords: |
Generating functions, finite groups of Lie type, maximal tori, symmetric group, hyperoctahedral group, signed permutation group, representation stability, homological stability |
| Subject: |
57T15, 05A15, 20G40, 20G05 |
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Abstract
In this paper we use generating function methods to obtain new asymptotic results about spaces of F-stable maximal tori in GLn(\overline{Fq}),
Sp2n(\overline{Fq}), and SO2n+1(\overline{Fq}). We recover stability results of Church-Ellenberg-Farb and Jiménez Rolland-Wilson for "polynomial'' statistics on these spaces, and we compute explicit formulas for their stable values. We derive a double generating function for the characters of the cohomology of flag varieties in type B/C, which we use to obtain analogs in type B/C of results of Chen: we recover "twisted homological stability'' for the spaces of maximal tori in
Sp2n(C) and SO2n+1(C), and we compute a generating function for their "stable twisted Betti numbers''. We also give a new proof of a result of Lehrer using symmetric function theory.
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| Acknowledgements
Fulman was partially supported by Simons Foundation grant 400528.
Jiménez Rolland is grateful for the financial support from PAPIIT-UNAM grant IA100816.
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| Author information
Jason Fulman:
Department of Mathematics, University of Southern California, Los Angeles, CA, United States 90089-2532
fulman@usc.edu
Rita Jiménez Rolland:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Oaxaca de Juárez, Oaxaca, México 68000
rita@im.unam.mx
Jennifer C. H. Wilson:
Department of Mathematics, Stanford University, Stanford, CA, United States 94305
jchw@stanford.edu
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