Related papers: Structure constants of shs$[\lambda]$: the deforme…
This article is the second in the series and is devoted to the type G_2. The work consists of two parts. In the first part we calculate the structure constants of the complex simple Lie algebra of type G_2. All structure constants are…
We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from…
Given a star product with separation of variables $\star$ on a pseudo-K\"ahler manifold $M$ and a point $x_0 \in M$, we construct an associative algebra of formal distributions supported at $x_0$. We use this algebra to express the formal…
In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in-detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra,…
We define the Higgs algebra $\mathcal{H}_\P1$ of the projective line, as a convolution algebra of constructible functions on the global nilpotent cone $\underline{\Lambda}_\P1$, a lagrangian substack of the Higgs bundle $T^*\Coh_\P1$, where…
Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra -- the…
he analytic formulas for structure constants of $su(2S+1)$ algebra in terms of $3jm$ and $6j$ symbols of $su(2)$ have been derived for the decomplexification of the Liouville-von Neumann equation.
Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on the level of the pairwise commuting…
Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semi-simple Lie algebras with respect to formal deformations is…
We introduce a generalization of the Heisenberg algebra which is written in terms of a functional of one generator of the algebra, $f(J_0)$, that can be any analytical function. When $f$ is linear with slope $\theta$, we show that the…
We investigate the Weyl-Wigner-Gr\"oenewold-Moyal, the Stratonovich and the Berezin group quantization schemes for the space-space noncommutative Heisenberg-Weyl group. We show that the $\star$-product for the deformed algebra of Weyl…
We define a three-parameter deformation of the Weyl-Heisenberg algebra that generalizes the q-oscillator algebra. By a purely algebraical procedure, we set up on this quantum space two differential calculi that are shown to be invariant on…
The immaculate functions, $\mathfrak{S}_{\alpha}$, were introduced as a Schur-like basis for $\operatorname{\mathsf{Nsym}}$. We investigate facts about their structure constants. These are analogues of Littlewood-Richardson coefficents. We…
The algebra S of symmetric invariants over the field with two elements is an unstable algebra over the Steenrod algebra A, and is isomorphic to the mod two cohomology of BO, the classifying space for vector bundles. We provide a minimal…
We give a solution to the long-standing problem of constructing the generators of hidden symmetries of the quantum Higgs oscillator, a particle on a d-sphere moving in a central potential varying as the inverse cosine-squared of the polar…
We discuss classical integrable structure of two-dimensional sigma models which have three-dimensional Schrodinger spacetimes as target spaces. The Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The original AdS_3…
We study structure constants of local operators inserted on the Wilson loop in ${\cal N}=4$ super Yang-Mills theory. We compute the structure constants in the SU(2) sector at tree level using the correspondence between operators on the…
The space spanned by the characters of twisted affine Lie algebras admit the action of certain congruence subgroups of $SL(2,\mathbb{Z})$. By embedding the characters in the space spanned by theta functions, we study an…
We study the degeneration relations on the varieties of associative and Lie algebra structures on a fixed finite dimensional vector space and give a description of them in terms of Gerstenhaber formal deformations. We use this result to…
We found hermitian realizations of the position vector $\vec{r}$, angular momentum $\vec{\Lambda}$ and linear momentum $\vec{p}$ behaving like vectors with respect to the $SU_q(2)$ algebra, generated by $L_0$ and $L_\pm$. They are used to…