Dongho Moon

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The Iwahori-Hecke algebra Hk(q ) 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 Hk(q ) 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 construct(More)
The factorization theorem by King, Tollu and Toumazet gives four different reduction formulae of LittlewoodRichardson 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 reduction(More)
There are two well known reduction formulae for structural constants of the cohomology ring of Grassmannians, i.e., LittlewoodRichardson 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)
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)
The nonelliptic A2-webs with k “+”s on the top boundary and 3n − 2k “−”s on the bottom boundary combinatorially model the space Homsl3(V,V) of sl3-module maps on tensor powers of the natural 3-dimensional sl3-module V, and they have connections with the combinatorics of Springer varieties. Petersen, Pylyavskyy, and Rhodes showed that the set of such A2-webs(More)
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