A motivated proof of the Gollnitz-Gordon-Andrews identities

被引：5

作者：

Coulson, Bud ^{[1
]}

Kanade, Shashank ^{[1
,2
]}

Lepowsky, James ^{[1
]}

McRae, Robert ^{[1
,3
]}

Qi, Fei ^{[1
]}

Russell, Matthew C. ^{[1
]}

Sadowski, Christopher ^{[1
,4
]}

机构：

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[3] Peking Univ, Beijing Int Ctr Math Res, Beijing 100084, Peoples R China

[4] Ursinus Coll, Dept Math & Comp Sci, Collegeville, PA 19426 USA

来源：

RAMANUJAN JOURNAL | 2017年 / 42卷 / 01期

关键词：

Gollnitz-Gordon-Andrews identities; Partition identities; Vertex operator algebras; VERTEX-ALGEBRAIC STRUCTURE; PRINCIPAL SUBSPACES; STANDARD MODULES; RAMANUJAN; A(1)((1))-MODULES;

D O I：

10.1007/s11139-015-9722-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present what we call a "motivated proof" of the Gollnitz-Gordon-Andrews identities. A similar motivated proof of the Rogers-Ramanujan identities was previously given by G. E. Andrews and R. J. Baxter, and was subsequently generalized to Gordon's identities by J. Lepowsky and M. Zhu. We anticipate that the present proof of the Gollnitz-Gordon-Andrews identities will illuminate certain twisted vertex-algebraic constructions.

引用

页码：97 / 129

页数：33

共 50 条

[31] On the Andrews-Schur proof of the Rogers-Ramanujan identities
Chan, Hei-Chi
RAMANUJAN JOURNAL, 2010, 23 (1-3): : 417 - 431
[32] Cylindric partitions, Wr characters and the Andrews-Gordon-Bressoud identities
Foda, O.
Welsh, T. A.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2016, 49 (16)
[33] Andrews-Gordon type identities from combinations of Virasoro characters
Feigin, Boris
Foda, Omar
Welsh, Trevor
RAMANUJAN JOURNAL, 2008, 17 (01): : 33 - 52
[34] AN ANALYTIC PROOF OF ROGERS-RAMANUJAN-GORDON IDENTITIES
ANDREWS, GE
AMERICAN JOURNAL OF MATHEMATICS, 1966, 88 (04) : 844 - &
[35] Structure of certain level 2 standard modules for A5(2) and the Gollnitz-Gordon identities
Kanade, Shashank
RAMANUJAN JOURNAL, 2018, 45 (03): : 873 - 893
[36] The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators
Capparelli, S.
Lepowsky, J.
Milas, A.
RAMANUJAN JOURNAL, 2006, 12 (03): : 379 - 397
[37] SOME FORMULAS RELATED TO DILOGARITHMS, THE ZETA FUNCTION AND THE ANDREWS-GORDON IDENTITIES
RICHMOND, B
SZEKERES, G
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1981, 31 (OCT): : 362 - 373
[38] An identity of Andrews and a new method for the Riordan array proof of combinatorial identities
Brietzke, Eduardo H. M.
DISCRETE MATHEMATICS, 2008, 308 (18) : 4246 - 4262
[39] Some partition and analytical identities arising from the Alladi, Andrews, Gordon bijection
S. Capparelli
A. Del Fra
P. Mercuri
A. Vietri
The Ramanujan Journal, 2022, 57 : 175 - 188
[40] Some partition and analytical identities arising from the Alladi, Andrews, Gordon bijection
Capparelli, S.
Del Fra, A.
Mercuri, P.
Vietri, A.
RAMANUJAN JOURNAL, 2022, 57 (01): : 175 - 188

← 1 2 3 4 5 →