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We study the structure of various invariants of the symmetric powers of a smooth projective curve in terms of that of the Jacobian of the curve. We generalise the results of Macdonald and Collino to various invariants including the…
We consider the $N\!=\!1$ supersymmetric $\sigma$-model and we examine the transformation properties of the partition function under target-space duality. Contrary to what one would expect, we find that it is not, in general, invariant. In…
Fermionic-type character formulae are presented for charged irreduciblemodules of the graded parafermionic conformal field theory associated to the coset $osp(1,2)_k/u(1)$. This is obtained by counting the weakly ordered `partitions'…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Particular complexity of linear quantum optical networks is deserved recently certain attention due to possible implications for theory of quantum computation. Two relevant models of bosons are discussed in presented work. Symmetric product…
We prove a variety of results describing the possible diagonals of tuples of commuting hermitian operators in type $II_1$ factors. These results are generalisations of the classical Schur-Horn theorem to the infinite dimensional,…
The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…
We consider the quantum theory of the Lorentzian fermionic differential forms and the corresponding bi-spinor quantum fields, which are the expansion coefficients of the forms in the bi-spinor basis of Becher and Joos [7]. The canonical…
The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed…
We consider a Moyal plane and propose to make the noncommutativity parameter \Theta^{\mu\nu} bifermionic, i.e., composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which…
We analyze the universal transport behavior in 1D and 2D fermionic systems by following the unified framework provided by bosonization. The role played by the adiabatic transition between interacting and noninteracting regions is…
New generalized Poisson structures are introduced by using suitable skew-symmetric contravariant tensors of even order. The corresponding `Jacobi identities' are provided by conditions on these tensors, which may be understood as cocycle…
We show that a spectral wall, i.e., an obstacle in the dynamics of a bosonic soliton, which arises due to the transition of a normal mode into the continuum spectrum, exists after coupling the original bosonic model to fermions. This…
We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian…
We consider the symmetric group $S_n$-module of the polynomial ring with $m$ sets of $n$ commuting variables and $m'$ sets of $n$ anti-commuting variables and show that the multiplicity of an irreducible indexed by the partition $\lambda$…
We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the…
For quantum groups at a root of unity, there is a web of theorems (due to Bezrukavnikov and Ostrik, and relying on work of Lusztig) connecting the following topics: (i) tilting modules; (ii) vector bundles on nilpotent orbits; and (iii)…
Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular $j$ function can be reduced to the problem of…
Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, $\pi$-mesons, excitons, Cooper pairs are not ideal bosons, and,…
Covariant (Lorentz invariant) fracton matter, minimally coupled and charged under a symmetric rank two gauge tensor, is considered. The gauge transformations correspond to linearized longitudinal diffeomorphisms. Consistent possible…