Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)

Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of "mixed" products of Schur's S- and Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A_1^{(1)}. A realization of the basic representation that is of ``D_2^{(2)}''-type plays the central role.Comment: 21page

Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A(1)((1))

Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of "mixed" products of Schur's S- and Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A(1)((1)). A realization of the basic representation that is of "D-2((2))"-type plays the central role

A formula of Lascoux-Leclerc-Thibon and representations of symmetric groups

We consider Green polynomials at roots of unity, corresponding to partitions which we call $l$-partitions. We obtain a combinatorial formula for Green polynomials corresponding to $l$-partitions at primitive $l$-th roots of unity. The formula is rephrased in terms of representation theory of the symmetric group

A formula of Lascoux-Leclerc-Thibon and representations of symmetric groups

We consider Green polynomials at roots of unity, corresponding to partitions which we call $l$-partitions. We obtain a combinatorial formula for Green polynomials corresponding to $l$-partitions at primitive $l$-th roots of unity. The formula is rephrased in terms of representation theory of the symmetric group

Ethylene oxidation activity of silica-supported platinum catalysts for the preservation of perishables

The ethylene oxidation activities of silica-supported platinum-based catalysts (Pt/A380 and PtRu/A380) were studied under semi-practical conditions (liter-sized batch system containing moisture and perishables). Storage tests of premature bananas, cucumbers, and apples have proved that the catalysts can remove ethylene generated from the perishables. Ripening of these perishables is significantly delayed by the catalytic removal of ethylene, which confirms that these catalysts are effective for the extension of the shelf-lives of the perishables. Two crucial parameters, the rate of ethylene production from the perishables and the rate of ethylene decomposition by the catalysts, were successfully quantified through storage tests of the perishables. The minimum amount of catalyst necessary for practical application in a storage room can be estimated by a simple numerical analysis using the determined parameters