4 citations · 7 across the 3 of their papers we have counts for
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Root systems and diagram calculus. III. Semi-Coxeter orbits of linkage diagrams and the Carter theorem
Rafael Stekolshchik
A diagram obtained from the Carter diagram by adding one root together with its bonds such that the resulting subset of roots is linearly independent is said to be the {\it lin…
Kostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series
Rafael Stekolshchik
We generalize B. Kostant's construction of generating functions to the case of multiply-laced diagrams and we prove for this case W. Ebeling's theorem which connects the Poincare s…
Quadruples, admissible elements and Herrmann's endomorphisms
Rafael Stekolshchik
We obtain a connection between admissible elements for quadruples and Herrmann's endomorphisms. Herrmann constructed perfect elements , , in by means of s…
Notes on Coxeter Transformations and the McKay correspondence
Rafael Stekolshchik
We study in detail the Jordan forms of the Coxeter transformations and prove shearing formulas due to Subbotin and Sumin for the characteristic polynomials of the Coxeter transform…
On Admissible and Perfect Elements in the Modular Lattice
Rafael Stekolshchik
For the modular lattice D^4 = {1+1+1+1} associated with the extended Dynkin diagram \tilde{D}_4 (and also for D^r, where r > 4), Gelfand and Ponomarev introduced the notion of admi…