Supercharacters, symmetric functions in noncommuting variables, extended abstract

Marcelo Aguiar; Carlos André; Carolina Benedetti; Nantel Bergeron; Zhi Chen; Persi Diaconis; Anders Hendrickson; Samuel Hsiao; I. Martin Isaacs; Andrea Jedwab; Kenneth Johnson; Gizem Karaali; Aaron Lauve; Tung Le; Stephen Lewis; Huilan Li; Kay Magaard; Eric Marberg; Jean Christophe Novelli; Amy PANG; Franco Saliola; Lenny Tevlin; Jean Yves Thibon; Nathaniel Thiem; Vidya Venkateswaran; C. Ryan Vinroot; Ning Yan; Mike Zabrocki

doi:10.46298/dmtcs.2967

Supercharacters, symmetric functions in noncommuting variables, extended abstract

Marcelo Aguiar, Carlos André, Carolina Benedetti, Nantel Bergeron, Zhi Chen, Persi Diaconis, Anders Hendrickson, Samuel Hsiao, I. Martin Isaacs, Andrea Jedwab, Kenneth Johnson, Gizem Karaali, Aaron Lauve, Tung Le, Stephen Lewis, Huilan Li, Kay Magaard, Eric Marberg, Jean Christophe Novelli, Amy PANGFranco Saliola, Lenny Tevlin, Jean Yves Thibon, Nathaniel Thiem, Vidya Venkateswaran, C. Ryan Vinroot, Ning Yan, Mike Zabrocki

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

1 Citation (Scopus)

Abstract

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.

Original language	English
Title of host publication	23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Publisher	Maison de l'informatique et des mathematiques discretes
Pages	3-14
Number of pages	12
DOIs	https://doi.org/10.46298/dmtcs.2967
Publication status	Published - 1 Jan 2011

Publication series

Name	Discrete Mathematics & Theoretical Computer Science Proceedings
ISSN (Print)	1365-8050

User-Defined Keywords

supercharacters
set partitions
symmetric functions in non-commuting variables
Hopf algebras

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https://dmtcs.episciences.org/2967/pdf

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Aguiar, M., André, C., Benedetti, C., Bergeron, N., Chen, Z., Diaconis, P., Hendrickson, A., Hsiao, S., Isaacs, I. M., Jedwab, A., Johnson, K., Karaali, G., Lauve, A., Le, T., Lewis, S., Li, H., Magaard, K., Marberg, E., Novelli, J. C., ... Zabrocki, M. (2011). Supercharacters, symmetric functions in noncommuting variables, extended abstract. In 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (pp. 3-14). (Discrete Mathematics & Theoretical Computer Science Proceedings). Maison de l'informatique et des mathematiques discretes. https://doi.org/10.46298/dmtcs.2967

Aguiar, Marcelo ; André, Carlos ; Benedetti, Carolina et al. / Supercharacters, symmetric functions in noncommuting variables, extended abstract. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011). Maison de l'informatique et des mathematiques discretes, 2011. pp. 3-14 (Discrete Mathematics & Theoretical Computer Science Proceedings).

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title = "Supercharacters, symmetric functions in noncommuting variables, extended abstract",

abstract = "We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.",

keywords = "supercharacters, set partitions, symmetric functions in non-commuting variables, Hopf algebras",

author = "Marcelo Aguiar and Carlos Andr{\'e} and Carolina Benedetti and Nantel Bergeron and Zhi Chen and Persi Diaconis and Anders Hendrickson and Samuel Hsiao and Isaacs, {I. Martin} and Andrea Jedwab and Kenneth Johnson and Gizem Karaali and Aaron Lauve and Tung Le and Stephen Lewis and Huilan Li and Kay Magaard and Eric Marberg and Novelli, {Jean Christophe} and Amy PANG and Franco Saliola and Lenny Tevlin and Thibon, {Jean Yves} and Nathaniel Thiem and Vidya Venkateswaran and Vinroot, {C. Ryan} and Ning Yan and Mike Zabrocki",

year = "2011",

month = jan,

day = "1",

doi = "10.46298/dmtcs.2967",

language = "English",

series = "Discrete Mathematics & Theoretical Computer Science Proceedings",

publisher = "Maison de l'informatique et des mathematiques discretes",

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address = "France",

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Aguiar, M, André, C, Benedetti, C, Bergeron, N, Chen, Z, Diaconis, P, Hendrickson, A, Hsiao, S, Isaacs, IM, Jedwab, A, Johnson, K, Karaali, G, Lauve, A, Le, T, Lewis, S, Li, H, Magaard, K, Marberg, E, Novelli, JC, PANG, A, Saliola, F, Tevlin, L, Thibon, JY, Thiem, N, Venkateswaran, V, Vinroot, CR, Yan, N & Zabrocki, M 2011, Supercharacters, symmetric functions in noncommuting variables, extended abstract. in 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011). Discrete Mathematics & Theoretical Computer Science Proceedings, Maison de l'informatique et des mathematiques discretes, pp. 3-14. https://doi.org/10.46298/dmtcs.2967

Supercharacters, symmetric functions in noncommuting variables, extended abstract. / Aguiar, Marcelo; André, Carlos; Benedetti, Carolina et al.
23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011). Maison de l'informatique et des mathematiques discretes, 2011. p. 3-14 (Discrete Mathematics & Theoretical Computer Science Proceedings).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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AU - Aguiar, Marcelo

AU - André, Carlos

AU - Benedetti, Carolina

AU - Bergeron, Nantel

AU - Chen, Zhi

AU - Diaconis, Persi

AU - Hendrickson, Anders

AU - Hsiao, Samuel

AU - Isaacs, I. Martin

AU - Jedwab, Andrea

AU - Johnson, Kenneth

AU - Karaali, Gizem

AU - Lauve, Aaron

AU - Le, Tung

AU - Lewis, Stephen

AU - Li, Huilan

AU - Magaard, Kay

AU - Marberg, Eric

AU - Novelli, Jean Christophe

AU - PANG, Amy

AU - Saliola, Franco

AU - Tevlin, Lenny

AU - Thibon, Jean Yves

AU - Thiem, Nathaniel

AU - Venkateswaran, Vidya

AU - Vinroot, C. Ryan

AU - Yan, Ning

AU - Zabrocki, Mike

PY - 2011/1/1

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KW - set partitions

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BT - 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)

PB - Maison de l'informatique et des mathematiques discretes

ER -

Aguiar M, André C, Benedetti C, Bergeron N, Chen Z, Diaconis P et al. Supercharacters, symmetric functions in noncommuting variables, extended abstract. In 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011). Maison de l'informatique et des mathematiques discretes. 2011. p. 3-14. (Discrete Mathematics & Theoretical Computer Science Proceedings). doi: 10.46298/dmtcs.2967

Supercharacters, symmetric functions in noncommuting variables, extended abstract

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