Related papers: Matrix integrals and the geometry of spinors
This is a companion to a recent investigation of K-theoretical invariants for symmetric spaces. We introduce a new class of cycles in K-groups, which are connected to elements of an underlying root lattice. This will be needed for a…
An ensemble of 2 x 2 pseudo-Hermitian random matrices is constructed that possesses real eigenvalues with level-spacing distribution exactly as for the Gaussian Unitary Ensemble found by Wigner. By a re-interpretation of Connes' spectral…
We are interested in the harmonic analysis on $p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space $X$ of unitary hermitian matrices of odd size over a ${\mathfrak p}$-adic field of odd…
Inspired by recent formul\ae\ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants of $\mathbb{P}^1$ as an isomonodromic tau function associated with a difference equation. As a…
Bezrukavnikov-Finkelberg-Mirkovi\'c [Compos. Math. {\bf 141} (2005)] identified the equivariant $K$-group of an affine Grassmannian, that we refer as (the coordinate ring of) a BFM space \'a l\`a Teleman [Proc. ICM Seoul (2014)], with a…
In this paper, we develop a loop group description of harmonic maps $\mathcal{F}: M \rightarrow G/K$ ``of finite uniton type", from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type. This develops work of…
This work is developed in the context of Lorentzian spin-foams with space- and time-like boundaries. It is argued that the equations describing the semiclassical regime of the various spin-foam amplitudes admit a common biquaternionic…
In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be symplectic. This…
In the context of the two dimensional sigma model, we show that classical field theory naturally defines a functor from Segal's category of Riemann surfaces to the Guillemin-Sternberg/Weinstein category of canonical relations in symplectic…
The Bargmann-Fock space(or Fock space for short) is a fundamental example of reproducing kernel Hilbert spaces that has found fascinating applications across multiple fields of current interest, including quantum mechanics, time-frequency…
A variation of the Zamolodchikov-Faddeev algebra over a finite dimensional Hilbert space $\mathcal{H}$ and an involutive unitary $R$-Matrix $S$ is studied. This algebra carries a natural vacuum state, and the corresponding Fock…
We discuss a recipe to produce a lattice construction of fermionic phases of matter on unoriented manifolds. This is performed by extending the construction of spin TQFT via the Grassmann integral proposed by Gaiotto and Kapustin, to the…
We provide a determinantal formula for tau-functions of the KP hierarchy in terms of rectangular, constant matrices $A$, $B$ and $C$ satisfying a rank one condition. This result is shown to generalize and unify many previous results of…
We construct explicit complex-valued $p$-harmonic functions and harmonic morphisms on the classical compact symmetric complex and quaternionic Grassmannians. The ingredients for our construction method are joint eigenfunctions of the…
The perspective of Kac-Schwarz operators is introduced to the authors' previous work on the quantum mirror curves of topological string theory in strip geometry and closed topological vertex. Open string amplitudes on each leg of the web…
Given a symmetric triple $(G,K,\sigma)$ of compact type, with $G^{\sigma} = K$, the well known Cartan embedding $\hat{\Phi}: G/K \to G$ homothetically embeds the symmetric space $M = G/K$ as a totally geodesic submanifold of $G$. In this…
In this paper, we establish higher order Borel-Pompeiu formulas for conformally invariant fermionic operators in higher spin theory, which is the theory of functions on m-dimensional Euclidean space taking values in arbitrary irreducible…
Using methods from commutative algebra and topos-theory, we construct topos-theoretical points for the fppf topology of a scheme. These points are indexed by both a geometric point and a limit ordinal. The resulting stalks of the structure…
We develop a functorial framework for the ideal theory of commutative semirings using coherent frames and spectral spaces. Two central constructions-the radical ideal functor and the $k$-radical ideal functor-are shown to yield coherent…
We develop a new orbit equivalence framework for holomorphically mating the dynamics of complex polynomials with that of Kleinian surface groups. We show that the only torsion-free Fuchsian groups that can be thus mated are punctured sphere…