| Budget Amount *help |
¥3,830,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Research Abstract |
In the present research, we revealed a relationship between a representation of the Nichols-Woronowicz algebra describing the braided differential structure on the Weyl groups and the elliptic Dunkl operators. We also constructed the Nichols-Woronowicz model of the coinvariant algebras of the complex reflection groups. Moreover, a new Pieri-type formula for the torus-equivariant (quantum) cohomology ring of the flag variety has been proved by means of an extension of the Fomin-Kirillov quadratic lgebra. In the direction of research on Lefschetz properties, we gave a characterization of he Lefschetz elements in finite-dimensional Gorenstein algebras in terms of the Hessians f the corresponding polynomials. As an application, we constructed a new series of orenstein algebras without the strong Lefschetz property.
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