Restriction and induction for supercharacters of finite groups of triangular type
Sbornik. Mathematics, Tome 208 (2017) no. 7, pp. 977-991

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the restriction of any supercharacter of a finite group of triangular type to its subgroup is a sum of supercharacters with nonnegative integer coefficients. We define a superinduction and prove the analogue of Frobenius's reciprocity formula for supercharacters. Bibliography: 21 titles.
Keywords: supercharacter theory, triangular group, induced character, Frobenius reciprocity.
A. N. Panov. Restriction and induction for supercharacters of finite groups of triangular type. Sbornik. Mathematics, Tome 208 (2017) no. 7, pp. 977-991. http://geodesic.mathdoc.fr/item/SM_2017_208_7_a2/
@article{SM_2017_208_7_a2,
     author = {A. N. Panov},
     title = {Restriction and induction for supercharacters of finite groups of triangular type},
     journal = {Sbornik. Mathematics},
     pages = {977--991},
     year = {2017},
     volume = {208},
     number = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_7_a2/}
}
TY  - JOUR
AU  - A. N. Panov
TI  - Restriction and induction for supercharacters of finite groups of triangular type
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 977
EP  - 991
VL  - 208
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_7_a2/
LA  - en
ID  - SM_2017_208_7_a2
ER  - 
%0 Journal Article
%A A. N. Panov
%T Restriction and induction for supercharacters of finite groups of triangular type
%J Sbornik. Mathematics
%D 2017
%P 977-991
%V 208
%N 7
%U http://geodesic.mathdoc.fr/item/SM_2017_208_7_a2/
%G en
%F SM_2017_208_7_a2

[1] P. Diaconis, I. M. Isaacs, “Supercharacters and superclasses for algebra groups”, Trans. Amer. Math. Soc., 360:5 (2008), 2359–2392 | DOI | MR | Zbl

[2] C. A. M. André, “Basic characters of the unitriangular group”, J. Algebra, 175:1 (1995), 287–319 | DOI | MR | Zbl

[3] C. A. M. André, “Basic sums of coadjoint orbits of the unitriangular group”, J. Algebra, 176:3 (1995), 959–1000 | DOI | MR | Zbl

[4] C. A. M. André, “The basic character table of the unitriangular group”, J. Algebra, 241:1 (2001), 437–471 | DOI | MR | Zbl

[5] C. A. M. André, “The basic characters of the unitriangular group (for arbitrary primes)”, Proc. Amer. Math. Soc., 130:7 (2002), 1943–1954 | DOI | MR | Zbl

[6] Ning Yan, Representation theory of the finite unipotent linear groups, Ph.D. diss., Univ. of Pennsylvania, 2001, 41 pp. ; Representations of finite unipotent linear groups by the method of clusters, arXiv: 1004.2674 | MR

[7] J. L. Brumbaugh, M. Bulkow, P. S. Fleming, L. A. Garcia German, S. R. Garcia, G. Karaali, M. Michal, A. P. Turner, Hong Suh, “Supercharacters, exponential sums and the uncertainty principle”, J. Number Theory, 144 (2014), 151–175 | DOI | MR | Zbl

[8] C. F. Fowler, S. R. Garcia, G. Karaali, “Ramanujan sums as supercharacters”, Ramanujan J., 35:2 (2014), 205–241 | DOI | MR | Zbl

[9] N. Thiem, “Branching rules in the ring of superclass functions of unipotent upper-triangular matrices”, J. Algebraic Combin., 31:2 (2010), 267–298 | DOI | MR | Zbl

[10] N. Thiem, V. Venkateswaran, “Restricting supercharacters of the finite group of unipotent uppertriangular matrices”, Electron. J. Combin., 16:1 (2009), 23, 32 pp. | MR | Zbl

[11] E. Marberg, N. Thiem, “Superinduction for pattern groups”, J. Algebra, 321:12 (2009), 3681–3703 | DOI | MR | Zbl

[12] E. Arias-Castro, P. Diaconis, R. Stanley, “A super-class walk on upper-triangular matrices”, J. Algebra, 278:2 (2004), 739–765 | DOI | MR | Zbl

[13] A. O. F. Hendrickson, “Supercharacter theory costructions corresponding to Schur ring products”, Comm. Algebra, 40:12 (2012), 4420–4438 | DOI | MR | Zbl

[14] S. Andrews, “Supercharacter theories constructed by the method of little groups”, Comm. Algebra, 44:5 (2016), 2152–2179 | DOI | MR | Zbl

[15] M. Aguiar, C. André, C. Benedetti, N. Bergeron, Zhi Chen, P. Diaconis, A. Hendrickson, S. Hsiao, I. M. Isaacs, A. Jedwab, K. Johnson, G. Karaali, A. Lauve, Tung Le, S. Lewis, Huilan Li, K. Magaarg, E. Marberg, J.-Ch. Novelli, Amy Pang, F. Saliola, L. Tevlin, J.-Y. Thibon, N. Thiem, V. Venkateswaran, C. R. Vinroot, Ning Yan, M. Zabrocki, “Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras”, Adv. Math., 229:4 (2012), 2310–2337 | DOI | MR | Zbl

[16] A. N. Panov, “Teoriya superkharakterov dlya grupp obratimykh elementov privedennykh algebr”, Algebra i analiz, 27:6 (2015), 242–259 ; A. N. Panov, “Supercharacter theory for groups of invertible elements of reduced algebras”, St. Petersburg Math. J., 27:6 (2016), 1035–1047 ; arXiv: 1409.5565 | MR | Zbl | DOI

[17] A. N. Panov, “Supercharacters for the finite groups of triangular type”, Comm. Algebra (to appear)

[18] A. N. Panov, “Staroe i novoe v teorii superkharakterov konechnykh grupp”, Chebyshevskii sb., 16:4 (2015), 227–249

[19] R. S. Pierce, Associative algebras, Grad. Texts in Math., 88, Stud. Hist. Modern Sci., 9, Springer-Verlag, New York–Berlin, 1982, xii+436 pp. | DOI | MR | MR | Zbl | Zbl

[20] Ch. W. Curtis, I. Reiner, Representation theory of finite groups and associative algebras, Pure Appl. Math., 11, Interscience Publishers (John Wiley Sons), New York–London, 1962, xiv+685 pp. | MR | MR | Zbl

[21] J.-P. Serre, Représentations linéaires des groupes finis, Hermann, Paris, 1967, xii+135 pp. (not consecutively paged) | MR | Zbl | Zbl