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A q-weighted version of the Robinson-Schensted algorithm

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	A q-weighted version of the Robinson-Schensted algorithm
2.	Creator	Author's name, affiliation, country	Neil O'Connell; University of Warwick
2.	Creator	Author's name, affiliation, country	Yuchen Pei; University of Warwick
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	q-Whittaker functions; Macdonald polynomials;
3.	Subject	Subject classification	Primary 05E05, Secondary 15A52; 82C22
4.	Description	Abstract	We introduce a q-weighted version of the Robinson-Schensted (column insertion) algorithm which is closely connected to q Whittaker functions (or Macdonald polynomials with t=0) and reduces to the usual Robinson-Schensted algorithm when q=0. The q-insertion algorithm is `randomised', or `quantum', in the sense that when inserting a positive integer into a tableau, the output is a distribution of weights on a particular set of tableaux which includes the output which would have been obtained via the usual column insertion algorithm. There is also a notion of recording tableau in this setting. We show that the distribution of weights of the pair of tableaux obtained when one applies the q-insertion algorithm to a random word or permutation takes a particularly simple form and is closely related to q-Whittaker functions. In the case $0\le q<1$, the q-insertion algorithm applied to a random word also provides a new framework for solving the q-TASEP interacting particle system introduced (in the language of q-bosons) by Sasamoto and Wadati (1998) and yields formulas which are equivalent to some of those recently obtained by Borodin and Corwin (2011) via a stochastic evolution on discrete Gelfand-Tsetlin patterns (or semistandard tableaux) which is coupled to the q-TASEP. We show that the sequence of P-tableaux obtained when one applies the q-insertion algorithm to a random word defines another, quite different, evolution on semistandard tableaux which is also coupled to the q-TASEP.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	EPSRC
7.	Date	(YYYY-MM-DD)	2013-10-29
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2930
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2930
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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