caa a22 4500 606160930 CHVBK 20210128100632.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10468-015-9530-2 doi (NATIONALLICENCE)springer-10.1007/s10468-015-9530-2 Gerber Thomas Lehrstuhl D für Mathematik, RWTH., Pontdriesch 14-16, 52062, Aachen, Germany aut Crystal Isomorphisms in Fock Spaces and Schensted Correspondence in Affine Type A [Elektronische Daten] [Thomas Gerber] We are interested in the structure of the crystal graph of level l Fock spaces representations of $\mathcal{U}_{q}^{\prime} (\widehat{\mathfrak{s}\mathfrak{l}_{e}}) $ . Since the work of Shan (Ann. Sci. Éc Norm. Supér. 44:147-182, 2011), we know that this graph encodes the branching rule for a corresponding cyclotomic rational Cherednik algebra. Besides, it appears to be closely related to the Harish-Chandra branching graph for the appropriate finite unitary group, according to [8]. In this paper, we make explicit a particular isomorphism between connected components of the crystal graphs of Fock spaces. This so-called "canonical” crystal isomorphism turns out to be expressible only in terms of: Schensted's classic bumping procedure, the cyclage isomorphism defined in Jacon and Lecouvey (Algebras and Representation Theory 13:467-489, 2010), a new crystal isomorphism, easy to describe, acting on cylindric multipartitions. We explain how this can be seen as an analogue of the bumping algorithm for affine type A. Moreover, it yields a combinatorial characterisation of the vertices of any connected component of the crystal of the Fock space. Springer Science+Business Media Dordrecht, 2015 Algebraic combinatorics nationallicence Quantum groups nationallicence Ariki-Koike algebra nationallicence Cherednik algebra nationallicence Crystal graph nationallicence Robinson-Schensted correspondence nationallicence Algebras and Representation Theory Springer Netherlands 18/4(2015-08-01), 1009-1046 1386-923X 18:4<1009 2015 18 10468 https://doi.org/10.1007/s10468-015-9530-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9530-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gerber Thomas Lehrstuhl D für Mathematik, RWTH., Pontdriesch 14-16, 52062, Aachen, Germany aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/4(2015-08-01), 1009-1046 1386-923X 18:4<1009 2015 18 10468