1. Irreducible components of exotic Springer fibres II: The Exotic Robinson-Schensted algorithm
- Author
-
Daniele Rosso, Vinoth Nandakumar, and Neil Saunders
- Subjects
Nilpotent cone ,Mathematics::Combinatorics ,Group (mathematics) ,General Mathematics ,Flag (linear algebra) ,010102 general mathematics ,Extension (predicate logic) ,Type (model theory) ,01 natural sciences ,Symmetric group ,0103 physical sciences ,Bijection ,FOS: Mathematics ,010307 mathematical physics ,0101 mathematics ,Variety (universal algebra) ,Representation Theory (math.RT) ,Mathematics::Representation Theory ,QA ,Algorithm ,Mathematics - Representation Theory ,Mathematics - Abstract
Kato's exotic nilpotent cone was introduced as a substitute for the ordinary nilpotent cone of type C with cleaner properties. The geometric Robinson-Schensted correspondence is obtained by parametrizing the irreducible components of the Steinberg variety (the conormal variety for the action of a semisimple group on two copies of its flag variety); in type A the bijection coincides with the classical Robinson-Schensted algorithm for the symmetric group. Here we give a combinatorial description of the bijection obtained by using the exotic nilpotent cone instead of ordinary type C nilpotent cone in the geometric Robinson-Schensted correspondence; we refer this as the "exotic Robinson-Schensted bijection". This is interesting from a combinatorial perspective, and not a naive extension of the type A Robinson-Schensted bijection., Comment: 33 pages
- Published
- 2021