Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions

Henry Kvinge; Anthony M. Licata; Stuart Mitchell

Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions

Henry Kvinge, Anthony M. Licata, Stuart Mitchell

Mathematical Sciences Institute

Research output: Contribution to conference › Paper › peer-review

Abstract

We establish an isomorphism between the center End_H^'(1) of Khovanov's Heisenberg category H¹, the algebra λ° of shifted symmetric functions defined by Okounkov-Olshanski. We give a graphical description of the shifted power and Schur bases of λ^∗as elements of End_H'(1), and describe the curl generators of End_H1p1q in the language of shifted symmetric functions. This latter description makes use of the transition and co-transition measures of Kerov and the noncommutative probability spaces of Biane.

Original language	English
Publication status	Published - 2016
Event	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom Duration: 9 Jul 2017 → 13 Jul 2017

Conference

Conference	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
Country/Territory	United Kingdom
City	London
Period	9/07/17 → 13/07/17

Cite this

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title = "Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions",

abstract = "We establish an isomorphism between the center EndH'(1) of Khovanov's Heisenberg category H1, the algebra λ° of shifted symmetric functions defined by Okounkov-Olshanski. We give a graphical description of the shifted power and Schur bases of λ∗as elements of EndH'(1), and describe the curl generators of EndH1p1q in the language of shifted symmetric functions. This latter description makes use of the transition and co-transition measures of Kerov and the noncommutative probability spaces of Biane.",

keywords = "Asymptotic representation theory of symmetric groups, Heisenberg algebra categorification, Noncommutative probability theory, Shifted symmetric functions",

author = "Henry Kvinge and Licata, {Anthony M.} and Stuart Mitchell",

note = "Publisher Copyright: {\textcopyright} 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.; 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 ; Conference date: 09-07-2017 Through 13-07-2017",

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T1 - Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions

AU - Kvinge, Henry

AU - Licata, Anthony M.

AU - Mitchell, Stuart

PY - 2016

Y1 - 2016

N2 - We establish an isomorphism between the center EndH'(1) of Khovanov's Heisenberg category H1, the algebra λ° of shifted symmetric functions defined by Okounkov-Olshanski. We give a graphical description of the shifted power and Schur bases of λ∗as elements of EndH'(1), and describe the curl generators of EndH1p1q in the language of shifted symmetric functions. This latter description makes use of the transition and co-transition measures of Kerov and the noncommutative probability spaces of Biane.

AB - We establish an isomorphism between the center EndH'(1) of Khovanov's Heisenberg category H1, the algebra λ° of shifted symmetric functions defined by Okounkov-Olshanski. We give a graphical description of the shifted power and Schur bases of λ∗as elements of EndH'(1), and describe the curl generators of EndH1p1q in the language of shifted symmetric functions. This latter description makes use of the transition and co-transition measures of Kerov and the noncommutative probability spaces of Biane.

KW - Asymptotic representation theory of symmetric groups

KW - Heisenberg algebra categorification

KW - Noncommutative probability theory

KW - Shifted symmetric functions

UR - http://www.scopus.com/inward/record.url?scp=85091917944&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85091917944

T2 - 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017

Y2 - 9 July 2017 through 13 July 2017

ER -

Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions

Abstract

Conference

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