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Defect 2 spin blocks of symmetric groups and canonical basis coefficients.
- Source :
-
Representation Theory . 3/17/2022, Vol. 26, p134-178. 45p. - Publication Year :
- 2022
-
Abstract
- This paper addresses the decomposition number problem for spin representations of symmetric groups in odd characteristic. Our main aim is to find a combinatorial formula for decomposition numbers in blocks of defect 2, analogous to Richards's formula for defect 2 blocks of symmetric groups. By developing a suitable analogue of the combinatorics used by Richards, we find a formula for the corresponding "q-decomposition numbers", i.e. the canonical basis coefficients in the level-1 q-deformed Fock space of type A^{(2)}_{2n}; a special case of a conjecture of Leclerc and Thibon asserts that these coefficients yield the spin decomposition numbers in characteristic 2n+1. Along the way, we prove some general results on q-decomposition numbers. This paper represents the first substantial progress on canonical bases in type A^{(2)}_{2n}. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FOCK spaces
*SPIN-orbit interactions
*COMBINATORICS
Subjects
Details
- Language :
- English
- ISSN :
- 10884165
- Volume :
- 26
- Database :
- Academic Search Index
- Journal :
- Representation Theory
- Publication Type :
- Academic Journal
- Accession number :
- 155828861
- Full Text :
- https://doi.org/10.1090/ert/600