Related papers: Generalized Kazakov-Migdal-Kontsevich Model: group…
A simple lattice model inducing a gauge theory is considered. The model describes an interaction of a gauge field to an $N\times N$ complex matrix scalar field transforming as a field in the fundamental representation. In contrast to the…
Let $V$ be a finite-dimensional unitary representation of a compact quantum group $\mathrm{G}$ and denote by $\mathrm{G}_W$ the isotropy subgroup of a linear subspace $W\le V$ regarded as a point in the Grassmannian $\mathbb{G}(V)$. We show…
We define a new notion of cuspidality for representations of $\GL_n$ over a finite quotient $\Oh_k$ of the ring of integers $\Oh$ of a non-Archimedean local field $F$ using geometric and infinitesimal induction functors, which involve…
In the recently proposed generalization of the Yang-Mills theory the group of gauge transformation gets essentially enlarged. This enlargement involves an elegant mixture of the internal and space-time symmetries. The resulting group is an…
We reinterpret the Faddeev-Popov gauge-fixing procedure of Yang-Mills theories as the definition of a topological quantum field theory for gauge group elements depending on a background connection. This has the advantage of relating…
In a space of $d $ Grassmann coordinates two types of generators of Lorentz transformations can be defined, one of spinorial and the other of vectorial character. Both kinds of operators appear as linear operators in Grassmann space,…
A model is proposed which generates all oriented $3d$ simplicial complexes weighted with an invariant associated with a topological lattice gauge theory. When the gauge group is $SU_q(2)$, $q^n=1,$ it is the Turaev-Viro invariant and the…
We propose the Kazakov-Migdal model on graphs and show that, when the parameters of this model are appropriately tuned, the partition function is represented by the unitary matrix integral of an extended Ihara zeta function, which has a…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
We generalize Kontsevich's construction of L-infinity derivations of polyvector fields from the affine space to an arbitrary smooth algebraic variety. More precisely, we construct a map (in the homotopy category) from Kontsevich's graph…
We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil…
We introduce a new approach to representation theory of finite groups that uses some basic algebraic geometry and allows to do all the theory without using characters. With this approach, to any finite group $G$ we associate a finite number…
Chiral conformal blocks in a rational conformal field theory are a far going extension of Gauss hypergeometric functions. The associated monodromy representations of Artin's braid group capture the essence of the modern view on the subject,…
We introduce a parametrization of the coupling constant space of the generalized Kontsevich models in terms of a set of moments equivalent to those introduced recently in the context of topological gravity. For the simplest generalization…
We consider Faddeev formulation of general relativity in which the metric is composed of ten vector fields or a $4 \times 10$ tetrad. This formulation reduces to the usual general relativity upon partial use of the field equations. A…
For an $n$-fold Kazhdan--Patterson cover or Savin's cover of a general linear group over a non-archimedean local field of residual characteristic $p$ with $\mathrm{gcd}(n,p)=1$, we realize the Gelfand--Graev representation as a Hecke…
For any complex simple Lie algebra, we generalize primary fileds in the Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of irregular singularities and we construct integral representations of hypergeometric…
A generalised Amit-Roginsky vector model in flat space is obtained as the effective dynamics of pertubations around a classical solution of the Boulatov group field theory for 3d euclidean quantum gravity, extended to include additional…
Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…
We generalize the Marinari-Parisi definition for pure two dimensional quantum gravity $(k = 2)$ to all non unitary minimal multicritical points $(k \geq 3)$. The resulting interacting Fermi gas theory is treated in the collective field…