Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 1.4.2008 |
| Speaker: | Lenka Háková, FJFI, České vysoké učení technické |
| Title: | The rings of $n$-dimensional polytopes |
| Abstract: | (spoluautoři: J. Patera) Points of an orbit of a finite Coxeter group $G$, generated by $n$ reflections, are considered as vertices of a polytope ($G$-polytope) centered at origin of a real $n$-dimensional Euclidean space. A general efficient method is recalled for geometric description of $G$-polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of $G$-polytopes are introduced and their decompositon into the sums of $G$-polytopes is described. Several invariants of $G$-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers, and congruence classes of the polytopes. Examples and applications are shown. |
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