2009 Fiscal Year Final Research Report
Combinatorial structures of flag varieties and quantum deformation
| Project/Area Number |
19740013
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
MAENO Toshiaki Kyoto University, 大学院・工学研究科, 講師 (60291423)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 旗多様体 / 鏡映群 / Hopf代数 / Lefschetz性 |
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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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