15 citations · 55 across the 14 of their papers we have counts for
15 papers
Adjoints in symmetric squares of Lie algebra representations
Bruno Le Floch, Ilia Smilga
*Caveat: we learned post-factum that most of these results are not novel. We are keeping this paper for continuity reasons.* Given finite-dimensional complex representations an…
Action of on : the special case of
Ilia Smilga
In this note, we present an algorithm that allows to answer any individual instance of the following question. Let be a semisimple real Lie group, and an irred…
Geometrically and topologically random surfaces in a closed hyperbolic three manifold
Jeremy Kahn, Vladimir Markovic, Ilia Smilga
We study the distribution of geometrically and topologically nearly geodesic random surfaces in a closed hyperbolic 3-manifold M. In particular, we describe PSL(2,R) invariant meas…
Action of on for orthogonal and exceptional groups
Ilia Smilga
In this note, we present some results that partially answer the following question. Let be a simple real Lie group; what is the set of representations of in which the l…
New sequences of non-free rational points
Ilia Smilga
We exhibit some new infinite families of rational values of , some of them squares of rationals, for which the group or even the semigroup generated by the matrices $\left( \beg…
Action of the restricted Weyl group on the -invariant vectors of a representation
Ilia Smilga
This note constitutes a brief survey of our recent work on the problem of determining, for a given real Lie group~, the set of representations~ in which the longest element~$…
Proper actions of discrete groups of affine transformations
Jeffrey Danciger, Todd A. Drumm, William M. Goldman +1
In the early 1980's Margulis startled the world by showing the existence of proper affine actions of free groups on 3-space, answering a provocative and suggestive question Milnor…
Representations having vectors fixed by a Levi subgroup
Ilia Smilga
For any semisimple real Lie algebra , we classify the representations of that have at least one nonzero vector on which the centr…
Action of Weyl group on zero weight space
Bruno Le Floch, Ilia Smilga
For any simple complex Lie group we classify irreducible finite-dimensional representations for which the longest element of the Weyl group acts nontrivially on the zero…
Construction of Milnorian representations
Ilia Smilga
We prove a partial converse to the main theorem of the author's previous paper "Proper affine actions: a sufficient criterion" (submitted; available at arXiv:1612.08942). More prec…
Proper affine actions: a sufficient criterion
Ilia Smilga
For a semisimple real Lie group with an irreducible representation on a finite-dimensional real vector space , we give a sufficient criterion on for existence of a g…
Proper affine actions in non-swinging representations
Ilia Smilga
For a semisimple real Lie group with an irreducible representation on a finite-dimensional real vector space , we give a sufficient criterion on for existence of a g…
Proper affine actions on semisimple Lie algebras
Ilia Smilga
For any noncompact semisimple real Lie group , we construct a group of affine transformations of its Lie algebra whose linear part is Zariski-dense in $\operatorn…
Fundamental domains for properly discontinuous affine groups
Ilia Smilga
We construct a fundamental region for the action on the -dimensional affine space of some free, discrete, properly discontinuous groups of affine transformations preserving a…
Harmonic functions on the Sierpinski triangle
Ilia Smilga
In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle - more precisely, of their restriction to a side of the triangle. First…