Promotion and cyclic sieving via webs
T.Kyle Petersen
, Pavlo Pylyavskyy
and Brendon Rhoades
DOI: 10.1007/s10801-008-0150-3
Abstract
We show that Schützenberger's promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this action admits the cyclic sieving phenomenon.
Pages: 19–41
Keywords: keywords promotion; webs; cyclic sieving
Full Text: PDF
References
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2. Frenkel, I., Khovanov, M.: Canonical bases in tensor products and graphical calculus for Uq (sl2). Duke Math. J. 87, 409-480 (1997)
3. Haiman, M.: Dual equivalence with applications, including a conjecture of Proctor. Discrete Math. 99, 79-113 (1992)
4. Kuperberg, G.: Spiders for rank 2 Lie algebras. Commun. Math. Phys. 180(1), 109-151 (1996)
5. Kuperberg, G.: The quantum G2 link invariant. Internat. J. Math. 5(1), 61-85 (1994)
6. Khovanov, M., Kuperberg, G.: Web bases for sl(3) are not dual canonical. Pacific J. Math. 188(1), 129-153 (1999)
7. Lusztig, G.: Introduction to Quantum Groups. Birkhäuser, Boston (1993)
8. Martin, P.: Potts Models and Related Problems in Statistical Mechanics. World Scientific, Singapore (1991)
9. Morrison, S.: A Diagrammatic Category for the Representation Theory of Uq (sln), PhD thesis, UC