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The Iwahori-Hecke algebra H k (q 2) of type A acts on tensor product space V ⊗k of the natural representation of the quantum superalgebra Uq(gl(m, n)). We show this action of H k (q 2) and the action of Uq(gl(m, n)) on the same space determine commuting actions of each other. Together with this result and Gyoja's q-analogue of the Young symmetrizer, we(More)
The factorization theorem by King, Tollu and Toumazet gives four different reduction formulae of Littlewood-Richardson coefficients. One of them is the classical reduction formula of the first type while others are new. Moreover , the classical reduction formula of the second type is not a special case of KTT theorem. We give combinatorial proofs of(More)
There are two well known reduction formulae for structural constants of the cohomology ring of Grassmannians, i.e., Littlewood-Richardson coefficients. Two reduction formulae are a conjugate pair in the sense that indexing partitions of one formula are conjugate to those of the other formula. A nice bijective proof of the first reduction formula is given in(More)
The nonelliptic A 2-webs with k " + " s on the top boundary and 3n − 2k " − " s on the bottom boundary combinatorially model the space Hom sl 3 (V ⊗(3n−2k) , V ⊗k) of sl 3-module maps on tensor powers of the natural 3-dimensional sl 3-module V, and they have connections with the combinatorics of Springer varieties. Petersen, Pylyavskyy, and Rhodes showed(More)
There is a well-known classical reduction formula by Griffiths and Harris for Littlewood-Richardson coefficients, which reduces one part from each partition. In this article, we consider an extension of the reduction formula reducing two parts from each partition. This extension is a special case of the factorization theorem of Littlewood-Richardson(More)
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