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We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of…
We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal character rings of…
We apply the Izergin-Korepin analysis to the study of the projected wavefunctions of the generalized free-fermion model. We introduce a generalization of the $L$-operator of the six-vertex model by Bump-Brubaker-Friedberg and…
Bose-Einstein correlations of two identically charged $Q$-bosons are derived considering these particles to be confined in finite volumes. Boundary effects on single $Q$-boson spectrum are also studied. We illustrate the effects on the…
We study the computational complexity of quantum-mechanical expectation values of single-particle operators in bosonic and fermionic multi-particle product states. Such expectation values appear, in particular, in full-counting-statistics…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…
We introduce an affinization of the quantum Kac-Moody algebra associated to a symmetric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-Moody algebra by vertex operators from bosonic…
We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic tau function in a sense that generalizes Jimbo-Miwa-Ueno's. In order to achieve the generalization we need to define a…
A conjecture on the relation between the cubic Hodge integrals and the topological vertex in topological string theory is resolved. A central role is played by the notion of generalized shift symmetries in a fermionic realization of the…
Young's lattice is a prototypical example of differential posets. Differential posets have the Robinson correspondence, the correspondence between permutations and pairs of standard tableaux with the same shape, as in the case of Young's…
The partition function of composite bosons ("cobosons" for short) is calculated in the canonical ensemble, with the Pauli exclusion principle between their fermionic components included in an exact way through the finite temperature…
In the spirit of the generalized one-particle density matrix for fermions, we introduce generalized one- and two-particle density matrices to state representability conditions up to second order for boson systems without assuming particle…
Collective operators that describe interaction of generic quantum system with discrete spectrum with a quantum field are investigated. These operators, considered as operators in the entangled Fock space (space generated by action of…
We develop the theory of colored bosonic models (initiated by Borodin and Wheeler). We will show how a family of such models can be used to represent the values of Iwahori vectors in the "spherical model" of representations of $GL_r(F)$,…
Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less…
A new representation of the 2N fold integrals appearing in various two-matrix models that admit reductions to integrals over their eigenvalues is given in terms of vacuum state expectation values of operator products formed from…
We use a double shifted power analog of free fermion fields to introduce current operators, Hamiltonians, and vertex operators which are deformed by two families of parameters and satisfy analogous formulas to the classical case. We show…
The paper explains how a unit generalized quaternion is used to represent a rotation of a vector in 3-dimensional space. We review of some algebraic properties of generalized quaternions and operations between them and then show their…