Related papers: SL(3,C)-Character Varieties and RP2-Structures on …

We present the subalgebra structure of sl(3,O), a particular real form of e6 chosen for its relevance to particle physics and its close relation to generalized Lorentz groups. We use an explicit representation of the Lie group SL(3,O) to…

Type B 3-fold supersymmetry is a necessary and sufficient condition for a quantum Hamiltonian to admit three linearly independent local solutions in closed form. We show that any such a system is invariant under GL(3,C) homogeneous linear…

We introduce a geometric framework for constructing superintegrable systems from Poisson centralizers (commutants) in the Lie-Poisson algebra $S(\mathfrak{g})$ of a complex semisimple Lie algebra. Starting from a chain of reductive…

Let G be a Lie group and g its Lie algebra. We develop a theory of quasi Poisson structures relative to a not necessarily non-degenerate Ad-invariant symmetric 2-tensor in the tensor square of g and one of general not necessarily…

Four-dimensional supersymmetric N = 1 vacua of type IIB supergravity are elegantly described by generalized complex geometry. However, this approach typically obscures the SL(2, R) covariance of the underlying theory. We show how to rewrite…

We consider the space of bilinear forms on a complex N-dimensional vector space endowed with the quadratic Poisson bracket studied in our previous paper arXiv:1012.5251. We classify all possible quadratic brackets on the set of pairs of…

Supergroups are defined in the framework of $\dZ_2$-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex and real supergroups are defined by Brauer-Wall groups…

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra $\cA \subeq C^\infty(M)$ which has to satisfy a non-degeneracy condition…

Consider all moduli points corresponding with polarized abelian varieties in characteristic p such that the associated quasi-polarized p-divisible group is geometrically isomorphic with a given one. This defines a subset C of the moduli…

A two-generator Kleinian group $\langle f,g \rangle$ can be naturally associated with a discrete group $\langle f,\phi \rangle$ with the generator $\phi$ of order $2$ and where \begin{equation*} \langle f,\phi f \phi^{-1} \rangle= \langle…

We consider for structure groups ${\rm SU}(n)\,\subset\, {\rm SL}(n,\mathbb C)$ a densely defined toric structure on the moduli of framed parabolic sheaves on a three-punctured sphere, which degenerates to an actual toric structure. In…

Let (X, t, S) be a triple, where S is a compact, connected surface without boundary, and t is a free cellular involution on a CW-complex X. The triple (X, t, S) is said to satisfy the Borsuk-Ulam property if for every continuous map…

For a complex semi-simple group G and its real form G0 we define a Poisson structure on the flag variety of G such that all the Bruhat cells (for a suitable choice of a Borel subgroup of G) as well as all the G0-orbits are Poisson…

An SL_n-character of a group G is the trace of an SL_n-representation of G. We show that all algebraic relations between SL_n-characters of G can be visualized as relations between graphs (resembling Feynman diagrams) in any topological…

Let R be a non-commutative field. We prove that generic triples of flags in an m-dimensional R-vector space are described by flat R-line bundles on the honeycomb graph with (m-1)(m-2)/2 holes. Generalising this, we prove that…

Characters of rational vertex operator algebras (RVOAs) arising in 2-dimensional conformal field theories often belong (after suitable normalization) to the (multiplicative) semigroup E^+ of modular units whose Fourier expansions are in 1+q…

Let G be a connected, complex reductive Lie group with maximal compact subgroup K, and let X denote the moduli space of G- or K-valued representations of a rank r free group. In this article, we develop methods for studying the…

In this paper, we study the vector invariants, ${\bf{F}}[m V_2]^{C_p}$, of the 2-dimensional indecomposable representation $V_2$ of the cylic group, $C_p$, of order $p$ over a field ${\bf{F}}$ of characteristic $p$. This ring of invariants…

We classify SL(2;C)-representations of a Brieskorn homology 3-sphere. We show any irreducible representation into SL(2;C) is conjugate to that into either SU(2) or SL(2;R). We also give a construction of SL(2;R)-representations for a…

We show that mod $2$ cohomological invariants of the moduli stack $\mathscr{M}_{3,n}$ of smooth pointed curves of genus three contain a free module with generators in degree $0$, $2$, $3$, $4$ and $6$, formed by the invariants of the…