Graded Cartan determinants of the symmetric groups-Reference-Cited by-同舟云学术

Graded Cartan determinants of the symmetric groups

Published:2013-12-06 Issue:4 Volume:366 Page:2019-2040
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Tsuchioka Shunsuke

Abstract

We give the graded Cartan determinants of the symmetric groups. Based on that, we propose a gradation of Hill’s conjecture which is equivalent to Külshammer-Olsson-Robinson’s conjecture on the generalized Cartan invariants of the symmetric groups.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2014-366-04/S0002-9947-2013-05916-8/S0002-9947-2013-05916-8.pdf

Reference42 articles.

1. An integral PBW basis of the quantum affine algebra of type 𝐴⁽²⁾₂;Akasaka, Tatsuya;Publ. Res. Inst. Math. Sci.,2002

2. Combinatorics for graded Cartan matrices of the Iwahori-Hecke algebra of type 𝐴;Ando, Masanori;Ann. Comb.,2013

3. Representations of quantum algebras;Andersen, Henning Haahr;Invent. Math.,1991

4. Braid group action and quantum affine algebras;Beck, Jonathan;Comm. Math. Phys.,1994

5. An algebraic characterization of the affine canonical basis;Beck, Jonathan;Duke Math. J.,1999

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2. On graded Cartan invariants of symmetric groups and Hecke algebras;Mathematische Zeitschrift;2016-06-13

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