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Lapid and M\'{i}nguez gave a criterion of the irreducibility of the parabolic induction $\sigma \times \pi$, where $\sigma$ is a ladder representation and $\pi$ is an arbitrary irreducible representation of the general linear group over a…
All finite dimensional irreducible representations of the simple Lie-Kac super algebra SU(2/1) are explicitly constructed in the Chevalley basis as complex matrices. For typical representations, the distinguished Dynkin label is not…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra $H_n(q)$ of type $A_{n-1}$ in the non-generic case where $q$ is a root of unity. The approach is via the Specht modules of…
We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…
We discuss the structure of the Motzkin algebra $M_k(D)$ by introducing a sequence of idempotents and the basic construction. We show that $\cup_{k\geq 1}M_k(D)$ admits a factor trace if and only if $D\in \{2\cos(\pi/n)+1|n\geq 3\}\cup…
In this paper we have found irreducible representations (irreps) of the algebra of partially transposed permutation operators on last subsystem. We give here direct method of irreps construction for an arbitrary number of subsystems n and…
We construct the Lafforgue variety, an affine scheme equipped with an open dense subscheme parametrizing the simple modules of a non-commutative unital algebra $R$ over any field $k$, provided that the center $Z(R)$ is finitely generated…
This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…
We give a survey of several models of irreducible complementary series representations and their limits, special representations, for the groups SU(n,1) and SO(n,1), including new ones. These groups, whose geometrical meaning is well known,…
We study the structure of the category of representations of $\mathbf{FA}$, the category of finite sets and all maps, mostly working over a field of characteristic zero. This category is not semi-simple and exhibits interesting features. We…
We describe a method to construct irreducible baryon operators using all-to-all quark propagators. It was demonstrated earlier that a large basis of extended baryon operators on anisotropic, quenched lattices can be used to reliably extract…
We find decomposition series of length at most two for modular representations in positive characteristic of mapping class groups of surfaces induced by an integral version of the Witten-Reshetikhin-Turaev SO(3)-TQFT at the p-th root of…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
Manifestly consistent Fock representations of non-central (but ``core-central'') extensions of the $Z^N$-graded algebras of functions and vector fields on the $N$-dimensional torus $T^N$ are constructed by a kind of renormalization…
We construct an L^2-model of "very small" irreducible unitary representations of simple Lie groups G which, up to finite covering, occur as conformal groups Co(V) of simple Jordan algebras V. If $V$ is split and G is not of type A_n, then…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of SU(N), using the compact expressions of Hermitian Young…
Given a positive integer $n$ and a partition $(n_1,\ldots,n_r)$ of $n$, one can consider the associated $n$-dimensional multiprojective space $\mathbb{P}^{n_1}\times \cdots \times \mathbb{P}^{n_r}$. These multiprojective spaces are…
For a weighted graph $E$, we construct representation graphs $F$, and consequently, $L_K(E)$-modules $V_F$, where $L_K(E)$ is the Leavitt path algebra associated to $E$, with coefficients in a field $K$. We characterise representation…