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 (from-to) | 2310-2337 |
| Number of pages | 28 |
| Journal | Advances in Mathematics |
| Volume | 229 |
| Issue number | 4 |
| DOIs | |
| State | Published - Mar 1 2012 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras. / Aguiar, Marcelo; André, Carlos; Benedetti, Carolina; Bergeron, Nantel; Chen, Zhi; Diaconis, Persi; Hendrickson, Anders; Hsiao, Samuel; Isaacs, I. Martin; Jedwab, Andrea; Johnson, Kenneth; Karaali, Gizem; Lauve, Aaron; Le, Tung; Lewis, Stephen; Li, Huilan; Magaard, Kay; Marberg, Eric; Novelli, Jean Christophe; Pang, Amy; Saliola, Franco; Tevlin, Lenny; Thibon, Jean Yves; Thiem, Nathaniel; Venkateswaran, Vidya; Vinroot, C. Ryan; Yan, Ning; Zabrocki, Mike.
In: Advances in Mathematics, Vol. 229, No. 4, 01.03.2012, p. 2310-2337.Research output: Contribution to journal › Article
TY - JOUR
T1 - Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
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 - 2012/3/1
Y1 - 2012/3/1
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=84863069286&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84863069286&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2011.12.024
DO - 10.1016/j.aim.2011.12.024
M3 - Article
AN - SCOPUS:84863069286
VL - 229
SP - 2310
EP - 2337
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 4
ER -