We introduce the notion of standard (Kleshchev) multipartitions and establish a one-to-one correspondence between irreducible representations with integral weights for affine Hecke algebra type A parameter q?C× which is not root unity. then extend to all Kleshchev Ariki-Koike algebras type. By Schur–Weyl duality, we further this Drinfeld multipolynomials whose associated polynomial completely d...

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U q [osp(1/2)] and the corresponding supergroup OSp q (1/2). The classical q → 1 limit of this universal T matrix yields the group element of the undeformed OSp(1/2) supergroup. The finite dimensional representations of the quantum supergroup OSp q (1/2) are readily constructed emp...

We prove a duality relation for the generalized basic hypergeometric functions. It forms q-extension of recent result second- and third-named authors generalizes both q-hypergeometric identity due to author (jointly with Feng Yang) Heine’s $${}_2\phi _{1}$$ function Suzuki. further explore various consequences our leading several presumably new multi-term relations terminating non-terminating s...

We explore nonrelativistic limits of $\mathcal{N}=1$ quiver gauge theories in 5d. The stringy counterpart these Super Conformal Field Theories (SCFTs) is characterized by torsional string Newton-Cartan (TSNC) sigma models which are defined over non-Lorentzian manifolds. further show that under transverse T duality, TSNC mapped into another new class a T-dual background. Considering various fiel...

Abstract We reveal relations between the duality of capacities and Sobolev extendability Jordan domains in plane, explain how to read curve conditions involved via capacities. Finally as an application, we give alternative proof necessary condition for a planar domain be $$W^{1,\,q}$$ W 1</m...

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U q [osp(1/2)] and the corresponding su-pergroup OSp q (1/2). The finite dimensional representations of the quantum su-pergroup OSp q (1/2) are readily constructed employing the said universal T-matrix and the known finite dimensional representations of the dually related deformed ...

The q-rook monoid Rn(q) is a semisimple C(q)-algebra that specializes when q → 1 to C[Rn], where Rn is the monoid of n × n matrices with entries from {0, 1} and at most one nonzero entry in each row and column. We use a Schur-Weyl duality between Rn(q) and the quantum general linear group Uqgl(r ) to compute a Frobenius formula, in the ring of symmetric functions, for the irreducible characters...

Abstract Inspired by a recently proposed Duality and Conformal invariant modification of Maxwell theory (ModMax), we construct one-parameter family two-dimensional dynamical systems in classical mechanics that share many features with the ModMax theory. It consists couple $$\sqrt{T\overline{T}}$$ T...

Everybody knows from school how to solve a quadratic equation of the form $x^2-px+q=0$ graphically. But this method can become tedious if several equations ought be solved, as for each pair $(p,q)$ new parabola has drawn. Stunningly, there is one single curve that used every via drawing tangent lines through given point curve. In article we derive in an elementary way and generalize it $x^n-p...

Recently it was conjectured that parallel branes at conical singularities are related to string/M theory on AdS×X where X is an Einstein manifold. In this paper we consider coincident M2 branes near a conifold singularity when M theory is compactified on AdS4×Q for Q = (SU(2)×SU(2)× SU(2))/(U(1)× U(1)) as a seven dimensional Sasaki-Einstein manifold. We argue that M theory on AdS4 × Q can be de...