HOMFLY-PT and Alexander polynomials from a doubled Schur algebra

被引:2
作者
Queffelec, Hoel [1 ]
Sartori, Antonio [2 ]
机构
[1] Univ Montpellier, CNRS, IMAG, Montpellier, France
[2] Albert Ludwigs Univ Freiburg, Math Inst, Eckerstr 1, D-79104 Freiburg, Germany
关键词
Schur algebras; knot invariants; Alexander polynomial; HOMFLY-PT polynomial; Reshetikhin-Turaev invariants;
D O I
10.4171/QT/109
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We define a generalization of the Schur algebra which gives a unified setting for a quantum group presentation of the HOMFLY-PT polynomial, together with its specializations to the Alexander polynomial and to the sl(m) Reshetikhin-Turaev invariant.
引用
收藏
页码:323 / 347
页数:25
相关论文
共 18 条
  • [1] Webs and quantum skew Howe duality
    Cautis, Sabin
    Kamnitzer, Joel
    Morrison, Scott
    [J]. MATHEMATISCHE ANNALEN, 2014, 360 (1-2) : 351 - 390
  • [2] ON SCHUR ALGEBRAS AND RELATED ALGEBRAS .1.
    DONKIN, S
    [J]. JOURNAL OF ALGEBRA, 1986, 104 (02) : 310 - 328
  • [3] Doty S, 2002, INT MATH RES NOTICES, V2002, P1907
  • [4] On the defining relations for generalized q-Schur algebras
    Doty, Stephen
    Giaquinto, Anthony
    Sullivan, John
    [J]. ADVANCES IN MATHEMATICS, 2009, 221 (03) : 955 - 982
  • [5] A NEW POLYNOMIAL INVARIANT OF KNOTS AND LINKS
    FREYD, P
    YETTER, D
    HOSTE, J
    LICKORISH, WBR
    MILLETT, K
    OCNEANU, A
    [J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 12 (02) : 239 - 246
  • [6] Modified quantum dimensions and re-normalized link invariants
    Geer, Nathan
    Patureau-Mirand, Bertrand
    Turaev, Vladimir
    [J]. COMPOSITIO MATHEMATICA, 2009, 145 (01) : 196 - 212
  • [7] Gorsky E., 2013, ARXIV13043481MATHQA
  • [8] A generators and relations description of a representation category of Uq (gl(1|1))
    Grant, Jonathan
    [J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2016, 16 (01): : 509 - 539
  • [9] Jantzen J. C., 1996, GRADUATE STUDIES IN, V6
  • [10] Kassel C., 2008, GRADUATE TEXTS MATH, V247