Kronecker positivity and 2-modular representation theory
Copyright policy )Kronecker positivity and 2-modular representation theory
This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these results and other modular representation theoretic techniques on the study of Kronecker coefficients and hence verify Saxl’s conjecture for several large new families of partitions. In particular, we verify Saxl’s conjecture for all irreducible characters of S n \mathfrak {S}_n which are of 2-height zero.
- University of York United Kingdom
- Okinawa Institute of Science and Technology Japan
- White Rose Consortium: University of Leeds; University of Sheffield; University of York United Kingdom
- University of Hannover Germany
- University of Salford United Kingdom
Kronecker coefficients, Hecke algebra, Specht module, Representations of finite symmetric groups, Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik, Specht modul, Schur algebras, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory
Kronecker coefficients, Hecke algebra, Specht module, Representations of finite symmetric groups, Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik, Specht modul, Schur algebras, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory
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