Small-dimensional projective representations of symmetric and alternating groups

TL;DR

This paper classifies the smallest irreducible projective representations of symmetric and alternating groups, providing new bounds and insights into their dimensions and branching properties.

Contribution

It offers a classification of minimal and second minimal irreducible projective representations and establishes a lower bound for the third minimal dimension.

Findings

Classified minimal and second minimal irreducible projective representations

Established a lower bound for the third minimal dimension

Derived new results on branching of representations

Abstract

We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new results on branching which might be of independent interest.