Related papers: Bosonic formulas for $\hat{sl_2}$ coinvariants
We give a volume formula of hyperbolic knot complements using twisted Alexander invariants.
We compute the cone of effective divisors on a Bott-Samelson variety corresponding to an arbitrary sequence of simple roots. The main tool is a general result concerning effective cones of certain $B$-equivariant $\mathbb{P}^1$ bundles. As…
The covariant canonical method of quantization based on the De Donder-Weyl covariant canonical formalism is used to formulate a world-sheet covariant quantization of bosonic strings. To provide the consistency with the standard…
Roman logarithmic binomial formula analogue has been found . It is presented here also for the case of fibonomial coefficients which recently have been given a combinatorial interpretation by the present author.
We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given…
We discuss the modular invariance of the SL(2,R) WZW model. In particular, we discuss in detail the modular invariants using the \hat{sl}(2,R) characters based on the discrete unitary series of the SL(2,R) representations. The explicit…
In the note, the author discovers an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
Let B_{(l)} be the perfect crystal for the l-symmetric tensor representation of the quantum affine algebra U'_q(\hat{sl(n)}). For a partition mu = (mu_1,...,mu_m), elements of the tensor product B_{(mu_1)} \otimes ... \otimes B_{(mu_m)} can…
It is shown that all bosonic and fermionic massive string models admit consistent light-cone formulations. This result is used to derive the spin generating functions of these models in four dimensions.
We bosonize fermions by identifying their occupation numbers as the binary digits of a Bose occupation number. Unlike other schemes, our method allows infinitely many fermionic oscillators to be constructed from just one bosonic oscillator.
We define an $SL_2(\mathbb{R})$-Casson invariant of closed 3-manifolds. We also observe procedures of computing the invariants in terms of Reidemeister torsions. We discuss some approach of giving the Casson invariant some gradings.
We discuss self-adjoint operators given formally by expressions quadratic in bosonic creation and annihilation operators. We give conditions when they can be defined as self-adjoint operators, possibly after an infinite renormalization. We…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…
In this note, we construct invariant and coinvariant Morse chain complexes with integer coefficients for any compact effective orbifold. We show that the homologies of these two chain complexes are invariants of the orbifold. We conjecture…
We present an efficient method for computing the ${\rm SL}(3,\mathbb{C})$-character varieties of two-generator groups.
Binet formulae for three versions of third-order Pell polynomials are derived.
Continuous, SL($n$) and translation invariant real-valued valuations on Sobolev spaces are classified.
We derive a formula for the Dijkgraaf-Witten invariants of orientable Seifert 3-manifolds with orientable bases.
We discuss on very general grounds possible lineshapes of composite particles with one unstable constituent. Expressions are derived in a coupled-channel formalism for constituents interacting in an S-wave with no assumption made on the…
This paper defines versions of the Jones polynomial and Khovanov homology by using several maps from the set of Gauss diagrams to its variant. Through calculation of some examples, this paper also shows that these versions behave…