A Spin Analogue of Kerov Polynomials

Matsumoto, Sho

doi:10.3842/sigma.2018.053

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…Note that the free cumulants for strict partitions defined above and the ones considered by Matsumoto [Mat18] differ by a factor of 2. Figure 2 and Figure 3 shows that the measures σ ω ξ and σ ω D(ξ) are equal, up to a translation by 1 2 .…”

Section: Cumulants Of Charactersmentioning

confidence: 97%

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Random strict partitions and random shifted tableaux

Matsumoto

Śniady

2020

Sel. Math. New Ser.

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We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their shapes, provided that the representation character ratios and their cumulants converge to zero at some prescribed speed. Our class of examples includes uniformly random shifted standard tableaux with prescribed shape as well as shifted tableaux generated by some natural combinatorial algorithms (such as shifted Robinson-Schensted-Knuth correspondence) applied to a random input.2010 Mathematics Subject Classification. Primary 20C25; Secondary 20C30, 60F05, 05E10 .

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Section: Cumulants Of Charactersmentioning

confidence: 97%

“…Note that the free cumulants for strict partitions defined above and the ones considered by Matsumoto [Mat18] differ by a factor of 2. Proposition 4.9.…”

Section: Cumulants Of Charactersmentioning

confidence: 97%

Random strict partitions and random shifted tableaux

Matsumoto

Śniady

2020

Sel. Math. New Ser.

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“…Perhaps, we need to take into account more nonlocal effects than just a crossing of two strings. Let us remark that there are analogues of the Kerov conjecture under the Jack-deformed [Las09] and spin settings [Mat18,MŚ20].…”

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confidence: 99%

Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category

Koshida

2023

Journal of Combinatorial Theory, Series A

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Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category

Koshida¹

2021

Preprint

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In this paper, we study relationships between the normalized characters of symmetric groups and the Boolean cumulants of Young diagrams. Specifically, we show that each normalized character is a polynomial of twisted Boolean cumulants with coefficients being non-negative integers, and conversely that, when we expand a Boolean cumulant in terms of normalized characters, the coefficients are again nonnegative integers. The main tool is Khovanov's Heisenberg category and the recently established connection of its center to the ring of observables on Young diagrams, which enables one to apply graphical manipulations to computation of observables on Young diagrams. Therefore this paper is an attempt to deepen the connection between the asymptotic representation theory and the graphical categorification.

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A Spin Analogue of Kerov Polynomials

Cited by 4 publications

References 19 publications

Random strict partitions and random shifted tableaux

Random strict partitions and random shifted tableaux

Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category

Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category

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