50 citations · 80 across the 14 of their papers we have counts for
18 papers
Representations of the group of two-diagonal triangular matrices
Dmitry Fuchs, Alexandre Kirillov
Let G be a Lie group, - its Lie algebra, - the dual vector space and - the set of equivalence classes of unitary irreducible representations of .…
Differential geometry of space curves: Forgotten chapters
Dmitry Fuchs, Ivan Izmestiev, Matteo Raffaelli +2
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified trea…
Jordan types of triangular matrices over a finite field
Dmitry Fuchs, Alexandre Kirillov
Let be a partition of an integer and be a finite field of order . Let be the number of strictly upper triangular matrices of the Jor…
Cross-ratio dynamics on ideal polygons
Maxim Arnold, Dmitry Fuchs, Ivan Izmestiev +1
Two ideal polygons, and , in the hyperbolic plane or in hyperbolic space are said to be -related if the cross-ratio $[p_i,p_{i+1},q_i,q_{i+1…
Iterating evolutes of spatial polygons and of spatial curves
Dmitry Fuchs, Serge Tabachnikov
The evolute of a smooth curve in an m-dimensional Euclidean space is the locus of centers of its osculating spheres, and the evolute of a spatial polygon is the polygon whose conse…
On tangent cones of Schubert varieties
Dmitry Fuchs, Alexandre Kirillov, Sophie Morier-Genoud +1
We consider tangent cones of Schubert varieties in the complete flag variety, and investigate the problem when the tangent cones of two different Schubert varieties coincide. We gi…