Related papers: On Quasisymmetric Functions with Two Bordering Var…

In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $GL_n$. It is proved that functions corresponding to Gelfand-Tsetlin…

Motivated by the 1920's seminal work of Major MacMahon, Amdeberhan--Andrews--Tauraso recently introduced an infinite family of $q$-series \[ \mathcal{U}_{t}(a;q):= \sum_{1\le n_1<n_2<\cdots<n_t}…

Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper…

In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions,…

Let $M(\alpha)$ denote the (logarithmic) Mahler measure of the algebraic number $\alpha$. Dubickas and Smyth, and later Fili and the author, examined metric versions of $M$. The author generalized these constructions in order to associate,…

We construct a family of purely infinite $C^*$-algebras, $\mathcal{Q}^\lambda$ for $\lambda\in (0,1)$ that are classified by their $K$-groups. There is an action of the circle $\T$ with a unique ${\rm KMS}$ state $\psi$ on each…

We establish comparison maps between the classical algebraic $K$-theory of algebras over a field and its analogue $K^c$, an algebraic $K$-theory for coalgebras over a field. The comparison maps are compatible with the Hattori--Stallings…

A numerical semigroup is an additive subsemigroup of the non-negative integers. In this paper, we consider parametrized families of numerical semigroups of the form $P_n = \langle f_1(n), \ldots, f_k(n) \rangle$ for polynomial functions…

We define a new basis of quasisymmetric functions, the row-strict dual immaculate functions, as the generating function of a particular set of tableaux. We establish that this definition gives a function that can also be obtained by…

Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive…

Let $ \Omega \subset R^d $ have finite positive Lebesgue measure, and let $ \mathcal{L}^{2}(\Omega) $ be the corresponding Hilbert space of $ \mathcal{L}^{2} $-functions on $ \Omega $. We shall consider the exponential functions $…

We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…

Recently, Blasiak-Morse-Seelinger introduced symmetric functions called Katalan functions, and proved that the $K$-theoretic $k$-Schur functions due to Lam-Schilling-Shimozono form a subfamily of the Katalan functions. They conjectured that…

The noncommutative symmetric functions $\textbf{NSym}$ were first defined abstractly by Gelfand et al. in 1995 as the free associative algebra generated by noncommuting indeterminants $\{\boldsymbol{e}_n\}_{n\in \mathbb{N}}$ that were taken…

In this paper we present explicit product formulas for a continuous two-parameter family of Heckman-Opdam hypergeometric functions of type BC on Weyl chambers $C_q\subset \mathbb R^q$ of type $B$. These formulas are related to continuous…

We construct a two-parameter family of actions \omega_{k,a} of the Lie algebra sl(2,R) by differential-difference operators on R^N \setminus {0}. Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the…

The rational Cherednik algebra $\HH$ is a certain algebra of differential-reflection operators attached to a complex reflection group $W$. Each irreducible representation $S^\lambda$ of $W$ corresponds to a standard module $M(\lambda)$ for…

We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of…

The ring of symmetric functions occupies a central place in algebraic combinatorics, with a particularly notable role in Schubert calculus, where the standard cell decompositions of Grassmannians yield the celebrated family of Schur…

We study bounded and unbounded representations of the $*$-algebra $Q_{n,\lambda}(*)$ generated by $n$ idempotents whose sum equals $\lambda e$ ($\lambda\in{\mathbb C}$, $e$ is the identity).