Linear versus spin: representation theory of the symmetric groups

Abstract

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 $\xi$ with analogous normalized linear characters evaluated on the double partition $D(\xi )$. 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.

41 pages. Version 2: new text about non-oriented (but orientable) maps

References in corpus (7)

• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group
• Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula
• Random strict partitions and random shifted tableaux
• Asymptotic results for Representation Theory
• On random shifted standard Young tableaux and 132-avoiding sorting networks
• Stanley character formula for the spin characters of the symmetric groups

Cited by in corpus (3)

• Random strict partitions and random shifted tableaux
• Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category
• Symmetric group characters of almost square shape