Khovanov's Heisenberg Category, Moments in Free Probability, and Shifted Symmetric Functions
Séminaire lotharingien de combinatoire, 78B (2017)
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We establish an isomorphism between the center EndH'(1) of Khovanov's Heisenberg category H' and 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 EndH'(1) 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.
@article{SLC_2017_78B_a62,
author = {Henry Kvinge and Anthony M. Licata and Stuart Mitchell},
title = {Khovanov's {Heisenberg} {Category,} {Moments} in {Free} {Probability,} and {Shifted} {Symmetric} {Functions}},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {78B},
year = {2017},
url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a62/}
}
TY - JOUR AU - Henry Kvinge AU - Anthony M. Licata AU - Stuart Mitchell TI - Khovanov's Heisenberg Category, Moments in Free Probability, and Shifted Symmetric Functions JO - Séminaire lotharingien de combinatoire PY - 2017 VL - 78B PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a62/ ID - SLC_2017_78B_a62 ER -
%0 Journal Article %A Henry Kvinge %A Anthony M. Licata %A Stuart Mitchell %T Khovanov's Heisenberg Category, Moments in Free Probability, and Shifted Symmetric Functions %J Séminaire lotharingien de combinatoire %D 2017 %V 78B %I mathdoc %U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a62/ %F SLC_2017_78B_a62
Henry Kvinge; Anthony M. Licata; Stuart Mitchell. Khovanov's Heisenberg Category, Moments in Free Probability, and Shifted Symmetric Functions. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a62/