Superinduction for pattern groups
Name
Marberg-2009-Superinduction for p.pdf
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270.88 KB
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Adobe PDF
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Author(s)
Marberg, Eric
Thiem, Nathaniel
Date Issued
April 2009
Journal
Journal of Algebra
Publisher
Elsevier
Citation
Marberg, Eric, and Nathaniel Thiem. “Superinduction for Pattern Groups.” Journal of Algebra 321, no. 12 (June 2009): 3681–3703. © 2009 Elsevier Inc.
Version
Final published version
Abstract
It is well known that the representation theory of the finite group of unipotent upper-triangular matrices U[subscript n] over a finite field is a wild problem. By instead considering approximately irreducible representations (supercharacters), one obtains a rich combinatorial theory analogous to that of the symmetric group, where we replace partition combinatorics with set-partitions. This paper studies Diaconis–Isaacs' concept of superinduction in pattern groups. While superinduction shares many desirable properties with usual induction, it no longer takes characters to characters. We begin by finding sufficient conditions guaranteeing that superinduction is in fact induction. It turns out for two natural embeddings of U[subscript m] in U[subscript n], superinduction is induction. We conclude with an explicit combinatorial algorithm for computing this induction analogous to the Pieri-formulas for the symmetric group.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1016/j.jalgebra.2009.03.003
