Note on the permutation group associated to E-polynomials
DOI:
https://doi.org/10.13069/jacodesmath.1056485Keywords:
Centralizer algebra, Permutation groupAbstract
This is a continuation of our project which focuses on E-polynomials and the related combinatorics. A pair of groups appearing in the definition of E-polynomials yields the permutation group. In this paper, we determine the multi-matrix structures of the centralizer algebras of the tensor representations of this permutation group.
Received: 10 May 2020 | Accepted: 4 November 2021Downloads
References
E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin/Cummings, Menlo Park, CA (1984).
W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24(3-4) (1997) 235–265.
M. Broué and M. Enguehard, Polynômes des poids de certains codes et fonctions thêta de certains réseaux, Ann. Sci. Éc. Norm. Supér. (4) 5(1) (1972) 157–181.
W. Duke, On codes and Siegel modular forms, Int. Math. Res. Not. 1993(5) (1993) 125–136.
A. Hanaki, Association schemes on finite sets, online database, http://math.shinshu-u.ac.jp/~hanaki/as/, accessed on May 15, 2021.
M. Kosuda and M. Oura, On the centralizer algebras of the primitive unitary reflection group of order 96, Tokyo J. Math. 39(2) (2016) 469–482.
M. Kosuda and M. Oura, Centralizer algebras of the group associated to $\mathbb{Z}_4$-codes, Discrete Math. 340(10) (2017) 2437–2446.
T. Motomura and M. Oura, E-polynomials associated to $\mathbb{Z}_4$-codes, Hokkaido Math. J. 47(2) (2018) 339–350.
M. Oura, The dimension formula for the ring of code polynomials in genus 4, Osaka J. Math. 34(1) (1997) 53–72.
M. Oura, Eisenstein polynomials associated to binary codes, Int. J. Number Theory 5(4) (2009) 635–640.
M. Oura, Eisenstein polynomials associated to binary codes (II), Kochi J. Math. 11 (2016) 35–41.
M. Oura, Tables of weight enumerators, online resource, http://sphere.w3.kanazawa-u.ac.jp, accessed on May 15, 2021.
B. Runge, On Siegel modular forms. Part I, J. Reine Angew. Math. 436 (1993) 57–86.
B. Runge, On Siegel modular forms part II, Nagoya Math. J. 138 (1995) 179–197.
B. Runge, Codes and Siegel modular forms, Discrete Math. 148(1-3) (1996) 175–204.
C. C. Sims, Graphs and finite permutation groups, Math. Z. 95(1) (1967) 76–86.
H. Wielandt, Finite Permutation Groups, Academic Press, New York (1964).