Related papers: Unipotent quantum coordinate ring and cominuscule …

Drinfeld defined a unitarized R-matrix for any quantum group U_q(g). This gives a commutor for the category of U_q(g) representations, making it into a coboundary category. Henriques and Kamnitzer defined another commutor which also gives…

Let $\Omega \subset \mathbb{C}^m$ be an open, connected and bounded set and $\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on $\Omega$. In this article we study quotient Hilbert modules obtained from submodules,…

We construct by fusion product new irreducible representations of the quantum affinization $U_q(\hat{sl}_\infty)$. The action is defined via the Drinfeld coproduct and is related to the crystal structure of semi-standard tableaux of type…

We develop a fundamental theory of compact quantum group equivariant finite extensions of C*-algebras. In particular we focus on the case of quantum homogeneous spaces and give a Tannaka-Krein type result for equivariant correspondences. As…

Coquasitriangular universal ${\cal R}$ matrices on quantum Lorentz and quantum Poincar\'e groups are classified. The results extend (under certain assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on those objects…

Let U(g,e) be the finite W-algebra associated with a nilpotent element e in a simple Lie algebra g and assume that e is induced from a nilpotent element e_0 in a Levi subalgebra l of g. We show that if the finite W-algebra U(l,e_0) has a…

We introduce the notion of identity component of a compact quantum group and that of total disconnectedness. As a drawback of the generalized Burnside problem, we note that totally disconnected compact matrix quantum groups may fail to be…

For a smooth $p$-adic formal scheme over the ring of integers of a perfectoid field of mixed characteristic $(0,p)$ containing all $p$-power roots of unity, we prove that the prismatic cohomology of a locally finite free prismatic crystal…

Thirty years ago, Huneke (for local rings) and Lyubeznik (in general) conjectured that for all regular rings $R$, the local cohomology modules $H^i_I(R)$ have finitely many associated prime ideals. We prove substantial new cases of their…

We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, specialized at q=1, is semisimple. This implies that complex conjugation defines an algebra automorphism of the quantum cohomology ring localized…

Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental. This is a ring theoretic formulation of the well…

We give a classification of all irreducible completely pointed $U_q(\mathfrak{sl}_{n+1})$ modules over a characteristic zero field in which $q$ is not a root of unity. This generalizes the classification result of Benkart, Britten and…

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra $U_q(q(n))$. The key ingredients are the triangular decomposition of $U_q(q(n))$ and the classification of finite dimensional…

We introduce the notion of a crystal base of a finite dimensional q-deformed Kac module over the quantum superalgebra $U_q(\gl(m|n))$, and prove its existence and uniqueness. In particular, we obtain the crystal base of a finite dimensional…

The vector space \otimes^nC^2 upon which the XXZ Hamilonian with n spins acts bears the structure of a module over both the Temperley-Lieb algebra TL_n(\beta=q+1/q) and the quantum algebra U_qsl_2. The decomposition of \otimes^nC^2 as a…

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a…

We obtain the formula for intertwining operator(R-matrix) of quantum universal enveloping superalgebra U_qOSP(1,2) for U_qOSP(1,2)-Verma modules. By its restriction we obtain the R-matrix for two semiperiodic(semicyclic), two spin-j and…

In this paper we associate to every reduced C*-algebraic quantum group A a universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show that every *-representation of a modified L1-space is generated by a unitary…

It is shown that all important features of a $\mathrm{C}^*$-algebraic quantum group $(A,\Delta)$ defined by a modular multiplicative $W$ depend only on the pair $(A,\Delta)$ rather than the multiplicative unitary operator $W$. The proof is…

Let $R$ be a Noetherian commutative ring of dimension $n$, $A=R[X_1,\cdots,X_m]$ be a polynomial ring over $R$ and $P$ be a projective $A[T]$-module of rank $n$. Assume that $P/TP$ and $P_f$ both contain a unimodular element for some monic…