Séminaire Lotharingien de Combinatoire, 82B.33 (2019), 12 pp.
Judith Jagenteufel
A Sundaram type bijection for SO(2k+1): vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau
Abstract.
We present a bijection between vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau for the special orthogonal group SO(2k+1). This bijection is motivated by the direct-sum decomposition of the rth tensor power of the defining representation of SO(2k+1). To formulate it, we present an explicit formulation of Kwon's Littlewood-Richardson tableaux and find alternative tableaux with which they are in bijection.
Moreover we use a suitably defined descent set for vacillating tableaux to determine the quasi-symmetric expansion of the Frobenius characters of the isotypic components.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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