Related papers: Ore's theorem on subfactor planar algebras
We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group.…
A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of…
In this paper all of the classical constructions of A. Young are generalized to affine Hecke algebras of type A. It is proved that the calibrated irreducible representations of the affine Hecke algebra are indexed by placed skew shapes and…
The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function…
We extend some results of [BF12] on subfactor projections to show that the projection of a free factor B to the free factor complex of the free factor A is well-defined with uniformly bound diameter, unless either A is contained in B or A…
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…
In this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball $$\mathscr{D}=SO(2,n)/S(O(2) \times O(n))$$ and the corresponding holomorphic unitary (projective) representations of SO(2,n) on these…
Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group $G$ factors through a projective representation of $G$, except for some groups of Lie…
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
We present a purely planar algebraic proof of the main result of a paper of Guionnet-Jones-Shlaykhtenko which constructs an extremal subfactor from a subfactor planar algebra whose standard invariant is given by that planar algebra.
We prove an effective equidistribution theorem for orbits of certain unipotent subgroups in arithmetic quotients of perfect Lie groups with a polynomial error term. Even for semisimple quotients, our result provides the first infinite…
The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the question of whether a given representation is symplectic or…
We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II_1 factor,…
We prove a restricted projection theorem for an n-2 dimensional family of projections from $\mathbb R^n$ to $\mathbb R$. The family we consider arises naturally in the context of the adjoint representation of the maximal unipotent subgroup…
A brief proof of Lie's classification of solvable algebras of vector fields on the plane is given. The proof uses basic representation theory and PDEs.
We characterize when a subfactor $N\subseteq M$ is oracle computable relative to a presentation of the ambient factor $M$ in terms of computability of the Jones basic construction, in terms of computable Pismner-Popa bases, and in terms of…
Let $\M$ be a type ${\rm II_1}$ factor and let $\tau$ be the faithful normal tracial state on $\M$. In this paper, we prove that given finite elements $X_1,\cdots X_n \in \M$, there is a finite decomposition of the identity into $N \in…
The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to $Z$-transformation directed…
We give an identification between the planar algebra of the subgroup-subfactor $R \rtimes H \subset R \rtimes G$ and the $G$-invariant planar subalgebra of the planar algebra of the bipartite graph $\star_n$, where $n = [G : H]$. The…
Planar functions over finite fields give rise to finite projective planes and other combinatorial objects. They were originally defined only in odd characteristic, but recently Zhou introduced a definition in even characteristic which…