We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition with analogous normalized linear characters evaluated on the double partition . We also relate some natural filtration on the usual (linear) Kerov–Olshanski algebra of polynomial functions on the set of Young diagrams with its spin counterpart. Finally, we give a spin counterpart to Stanley formula for the characters of the symmetric groups in terms of counting maps.
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Keywords: Projective representations of the symmetric groups, linear representations of the symmetric groups, asymptotic representation theory, Stanley character formula
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@article{ALCO_2020__3_1_249_0,
author = {Matsumoto, Sho and \'Sniady, Piotr},
title = {Linear versus spin: representation theory of~the symmetric groups},
journal = {Algebraic Combinatorics},
pages = {249--280},
publisher = {MathOA foundation},
volume = {3},
number = {1},
year = {2020},
doi = {10.5802/alco.92},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.92/}
}
TY - JOUR AU - Matsumoto, Sho AU - Śniady, Piotr TI - Linear versus spin: representation theory of the symmetric groups JO - Algebraic Combinatorics PY - 2020 SP - 249 EP - 280 VL - 3 IS - 1 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.92/ DO - 10.5802/alco.92 LA - en ID - ALCO_2020__3_1_249_0 ER -
%0 Journal Article %A Matsumoto, Sho %A Śniady, Piotr %T Linear versus spin: representation theory of the symmetric groups %J Algebraic Combinatorics %D 2020 %P 249-280 %V 3 %N 1 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.92/ %R 10.5802/alco.92 %G en %F ALCO_2020__3_1_249_0
Matsumoto, Sho; Śniady, Piotr. Linear versus spin: representation theory of the symmetric groups. Algebraic Combinatorics, Volume 3 (2020) no. 1, pp. 249-280. doi : 10.5802/alco.92. https://alco.centre-mersenne.org/articles/10.5802/alco.92/
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