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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^\R$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the $G$-module structure of the homology of $X^\R$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type~$A$ and $B$, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.
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참고문헌 (31)
참고문헌 신청
H. Abe / 2015 / Young diagrams and intersection numbers for toric manifolds associated with Weyl chambers, Electron / J. Combin 22(2):24
A. Al-Raisi / 2014 / Equivariance, module structure, branched covers, strickland maps and co-homology related to the polyhedral product functor
A. Bahri / 2010 / The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces / Advances in Mathematics 225(3):1634~1668
Mark Benard / 1971 / On the Schur Indices of Characters of the Exceptional Weyl Groups / The Annals of Mathematics 94(1):89~107
Anders Björner / 1984 / Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings / Advances in Mathematics 52(3):173~212
A. Al-Raisi / 2014 / Equivariance, module structure, branched covers, strickland maps and co-homology related to the polyhedral product functor
A. Bahri / 2010 / The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces / Advances in Mathematics 225(3):1634~1668
Mark Benard / 1971 / On the Schur Indices of Characters of the Exceptional Weyl Groups / The Annals of Mathematics 94(1):89~107
Anders Björner / 1984 / Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings / Advances in Mathematics 52(3):173~212
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