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Duality and bicrystals on infinite binary matrices
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- The set of finite binary matrices of a given size is known to carry a finite type A bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums together with a natural generalisation of the 2M -- X Pitman transform. Next, we show that, once the relevant formalism on families of infinite binary matrices is introduced, this is a particular case of a much more general phenomenon. Each such family of matrices is proved to be endowed with Kac-Moody bicrystal and tricrystal structures defined from the classical root systems. Moreover, we give an explicit decomposition of these multicrystals, reminiscent of the decomposition of characters yielding the Cauchy identities.<br />Comment: 37 pages, 44 ref
- Subjects :
- Statistics and Probability
Algebra and Number Theory
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
FOS: Mathematics
Mathematics - Combinatorics
Discrete Mathematics and Combinatorics
Statistical and Nonlinear Physics
Combinatorics (math.CO)
Geometry and Topology
Representation Theory (math.RT)
Mathematics - Representation Theory
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....a57632fd89125ece7e67daa32c7f8977