Related papers: Multiplicities and tensor product coefficients for…

We develop a theory of weights for a quantum analogue of the symmetric pair (gl4,gl2 x gl2) realised as a quantum symmetric pair subalgebra. Based on Letzter's triangular decomposition we define Verma modules. Using magical operators that…

We show that the coefficients of decomposition into an irreducible components of the tensor powers of level $r$ symmetric algebra of adjoint representation coincide with the Verlinder numbers. Also we construct (for $sl(2)) the…

We develop a calculus based on graph enumeration for $S_n$-equivariant motivic invariants of graphically stratified moduli spaces. We apply our theory to the Deligne--Mumford moduli space $\overline{\mathcal{M}}_{g, n}$ and to the space of…

We consider $\mathcal{N}=2$ supersymmetric pure gauge theories on toric K\"ahler manifolds, with particular emphasis on $\mathbb{CP}^2$. By choosing a vector generating a $U(1)$ action inside the torus of the manifold, we construct…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

Many computational problems can be formulated in terms of high-dimensional functions. Simple representations of such functions and resulting computations with them typically suffer from the "curse of dimensionality", an exponential cost…

We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…

Let $T$ be a bilinear Calder\'on-Zygmund singular integral operator and $T^*$ be its corresponding truncated maximal operator. For any $b\in\text{BMO}(\mathbb {R}^n)$ and $\vec{b}=(b_1,\ b_2)\in\text{BMO}(\mathbb {R}^n)\times\text…

Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…

Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…

Let $k\ge 2$ be an integer and let $A$ be a set of nonnegative integers. For a $k$-tuple of positive integers $\underline{\lambda} = (\lambda_{1}, \dots{} ,\lambda_{k})$ with $1 \le \lambda_{1} < \lambda_{2} < \dots{} < \lambda_{k}$, we…

We investigate pointwise multipliers on vector-valued function spaces over $\mathbb{R}^d$, equipped with Muckenhoupt weights. The main result is that in the natural parameter range, the characteristic function of the half-space is a…

We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…

For arbitrary $n$ complex numbers $a_{\nu-1}$, $\nu=1,\dots,n$, where $n$ is sufficiently large, we get the representation in the form of power sums: $a_{\nu-1}=\lambda_1^\nu+\dots+\lambda_{2n+1}^\nu$, where $\lambda_k$ are distinct points,…

In this paper, the boundedness properties of vector-valued intrinsic square functions and their vector-valued commutators with $BMO(\mathbb R^n)$ functions are discussed. We first show the weighted strong type and weak type estimates of…

For a simple Lie algebra, over $\mathbb{C}$, we consider the weight which is the sum of all simple roots and denote it $\tilde{\alpha}$. We formally use Kostant's weight multiplicity formula to compute the "dimension" of the zero-weight…

We decompose the $\hat{\mathfrak{sl}}(n)$-module $V(\Lambda_0) \otimes V(\Lambda_i)$ and give generating function identities for the outer multiplicities. In the process we discover some seemingly new partition identities for $n=3, 4$.

The structure of r-fold tensor products of irreducible tame representations of the inductive limit U(\infty) of unitary groups U(n) are are described, versions of contragredient representations and invariants are realized on…

We introduce an algorithm to decompose orthogonal matrix representations of the symmetric group over the reals into irreducible representations, which as a by-product also computes the multiplicities of the irreducible representations. The…

Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…