publication . Preprint . Article . 2017

Symmetric group representations and Z

Anshul Adve; Alexander Yong;
Open Access English
  • Published: 30 Jun 2017
Abstract
We discuss implications of the following statement about the representation theory of symmetric groups: every integer appears infinitely often as an irreducible character evaluation, and every nonnegative integer appears infinitely often as a Littlewood-Richardson coefficient and as a Kronecker coefficient.
Subjects
free text keywords: Mathematics - Combinatorics, Representation theory, Mathematics, Pure mathematics, Symmetric group, Kronecker coefficient, Integer, Mathematical analysis
16 references, page 1 of 2

[BeSo98] N. Bergeron and F. Sottile, Schubert polynomials, the Bruhat order, and the geometry of flag manifolds, Duke Math. J. 95(1998), no. 2, 373-423.

[BlMuSo15] J. Blasiak, K. D. Mulmuley and M. Sohoni, Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem, Mem. Amer. Math. Soc., Vol. 235, No. 1109, 2015.

[BuSoYo05] A. S. Buch, F. Sottile and A. Yong, Quiver coefficients are Schubert structure constants, Math. Res. Lett. 12(2005), no. 4, 567-574.

[FePi11] V. Fe´ray and P. Sniady, Asymptotics of characters of symmetric groups related to Stanley character formula, Ann. Math., Vol 173(2011), Issue 2, 887-906.

[FuHa99] W. Fulton and J. Harris, Representation theory, a first course, Springer-Verlag, 1999.

[Ja78] G. D. James, The Representation Theory of the Symmetric Groups, Lecture Notes in Mathematics, Volume 682, Springer, 1978.

[JaKe09] G. D. James and A. Kerber, The Representation Theory of the Symmetric Group, Cambridge University Press, Cambridge, 2009.

[KnMiSh04] A. Knutson, E. Miller and M. Shimozono, Four positive formulae for type A quiver polynomials, Invent. Math. 166(2006), no. 2, 229-325.

[Ma01] L. Manivel, Symmetric functions, Schubert polynomials and degeneracy loci. Translated from the 1998 French original by John R. Swallow. SMF/AMS Texts and Monographs, American Mathematical Society, Providence, 2001.

[Mu38] F. D. Murnaghan, The analysis of the Kronecker product of irreducible representations of the symmetric group, Amer. J. Math. 60(1938), no. 3, 761-784.

[Na06] H. Narayanan, On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients, J. Alg. Comb., Vol. 24, N. 3, 2006, 347-354.

[Po99] P. Polo, Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups, Represent. Theory. 3(1999), 90-104.

[Ro96] Y. Roichman, Upper bound on the characters of the symmetric groups, Invent. Math., Vol 125 (1996), Issue 3, 451-485. [OpenAIRE]

[Sa01] B. Sagan, The symmetric group, Second edition, Graduate Texts in Mathematics, 203. SpringerVerlag, New York, 2001.

[St99] R. P. Stanley, Enumerative Combinatorics, Volume 2, Cambridge University Press, 1999.

16 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Preprint . Article . 2017

Symmetric group representations and Z

Anshul Adve; Alexander Yong;