A graphical calculus for the Jack inner product on symmetric functions

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:155

Article

Licata, Anthony¹  Rosso, Daniele²  Savage, Alistair³ 

[1] Australian Natl Univ, Math Sci Inst, Canberra, ACT, Australia

[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

[3] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

关键词: Symmetric functions;    Jack inner product;    Categorification;    Heisenberg algebra;    Graded Frobenius superalgebra;    Fock space;    Wreath product algebra;   

DOI  :  10.1016/j.jcta.2017.11.020

来源: Elsevier

【 摘 要 】

Starting from a graded Frobenius superalgebra B, we consider a graphical calculus of B-decorated string diagrams. From this calculus we produce algebras consisting of closed planar diagrams and of closed annular diagrams. The action of annular diagrams on planar diagrams can be used to make clockwise (or counterclockwise) annular diagrams into an inner product space. Our main theorem identifies this space with the space of symmetric functions equipped with the Jack inner product at Jack parameter dim B-even - dim B-odd. In this way, we obtain a graphical realization of that inner product space. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free