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

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

Division of Engineering and Science (Abington)

Research output: Contribution to conference › Paper › peer-review

1 Scopus citations

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 (US)
Pages	3-14
Number of pages	12
State	Published - 2011
Event	23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11 - Reykjavik, Iceland Duration: Jun 13 2011 → Jun 17 2011

Conference

Conference	23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11
Country/Territory	Iceland
City	Reykjavik
Period	6/13/11 → 6/17/11

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Cite this

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. 3-14. Paper presented at 23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11, Reykjavik, Iceland.

@conference{76058a32e9f14d8d8c53a64a37cf0678,

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.",

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",

note = "Funding Information: diaconis@math.stanford.edu (P. Diaconis), ahendric@cord.edu (A. Hendrickson), hsiao@bard.edu (S. Hsiao), isaacs@math.wisc.edu (I.M. Isaacs), jedwab@usc.edu (A. Jedwab), kwj1@psu.edu (K. Johnson), gizem.karaali@pomona.edu (G. Karaali), lauve@math.luc.edu (A. Lauve), lttung96@yahoo.com (T. Le), stedalew@u.washington.edu (S. Lewis), huilan.li@gmail.com (H. Li), k.magaard@bham.ac.uk (K. Magaard), emarberg@math.mit.edu (E. Marberg), novelli@univ-mlv.fr (J.-C. Novelli), amypang@stanford.edu (A. Pang), saliola@gmail.com (F. Saliola), ltevlin@nyu.edu (L. Tevlin), jyt@univ-mlv.fr (J.-Y. Thibon), thiemn@colorado.edu (N. Thiem), vidyav@caltech.edu (V. Venkateswaran), vinroot@math.wm.edu (C.R. Vinroot), ning.now@gmail.com (N. Yan), zabrocki@mathstat.yorku.ca (M. Zabrocki). 1 Supported by NSF DMS-1001935. 2 Supported by CRC and Beca Mazda. 3 Supported by CRC and NSERC. 4 Supported by NSF DMS-0804324. 5 Supported by NSF DMS 07-01291. 6 Supported by NSA H98230-10-1-0362. 7 Supported by NSF DMS-0854893. 8 Supported by NSF DMS-0652641. 9 Supported by NDSEG Fellowship. 10 Supported by CRC. 11 Supported by NSF DMS-0854849. 12 Supported by NSERC.; 23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11 ; Conference date: 13-06-2011 Through 17-06-2011",

year = "2011",

language = "English (US)",

pages = "3--14",

}

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', Paper presented at 23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11, Reykjavik, Iceland, 6/13/11 - 6/17/11 pp. 3-14.

TY - CONF

T1 - Supercharacters, symmetric functions in noncommuting variables, extended abstract

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

N1 - Funding Information: diaconis@math.stanford.edu (P. Diaconis), ahendric@cord.edu (A. Hendrickson), hsiao@bard.edu (S. Hsiao), isaacs@math.wisc.edu (I.M. Isaacs), jedwab@usc.edu (A. Jedwab), kwj1@psu.edu (K. Johnson), gizem.karaali@pomona.edu (G. Karaali), lauve@math.luc.edu (A. Lauve), lttung96@yahoo.com (T. Le), stedalew@u.washington.edu (S. Lewis), huilan.li@gmail.com (H. Li), k.magaard@bham.ac.uk (K. Magaard), emarberg@math.mit.edu (E. Marberg), novelli@univ-mlv.fr (J.-C. Novelli), amypang@stanford.edu (A. Pang), saliola@gmail.com (F. Saliola), ltevlin@nyu.edu (L. Tevlin), jyt@univ-mlv.fr (J.-Y. Thibon), thiemn@colorado.edu (N. Thiem), vidyav@caltech.edu (V. Venkateswaran), vinroot@math.wm.edu (C.R. Vinroot), ning.now@gmail.com (N. Yan), zabrocki@mathstat.yorku.ca (M. Zabrocki). 1 Supported by NSF DMS-1001935. 2 Supported by CRC and Beca Mazda. 3 Supported by CRC and NSERC. 4 Supported by NSF DMS-0804324. 5 Supported by NSF DMS 07-01291. 6 Supported by NSA H98230-10-1-0362. 7 Supported by NSF DMS-0854893. 8 Supported by NSF DMS-0652641. 9 Supported by NDSEG Fellowship. 10 Supported by CRC. 11 Supported by NSF DMS-0854849. 12 Supported by NSERC.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84860472062&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860472062&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84860472062

SP - 3

EP - 14

T2 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11

Y2 - 13 June 2011 through 17 June 2011

ER -

Supercharacters, symmetric functions in noncommuting variables, extended abstract

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