Related papers: Power sum elements in the $G_2$ skein algebra

2-Dim quantum Poincare` Group E_q(1,1) at roots of unity, its dual U_q(e(1,1)) and some of its homogeneous spaces are introduced. Invariant integrals on E_q(1,1) and its invariant discrete subgroup E(1,1\mid p) are constructed.…

Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are important from a physical point of view…

We study the behavior of the Witten-Reshetikhin-Turaev SU(2) invariants of links in L(p,q) as a function of the level r-2. They are given by 1 over the square root of r times one of p Laurent polynomials evaluated at e to the 2 pi i divided…

We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{\Sigma,\mathbb{W}}^{A}$ of a walled surface $(\Sigma,\mathbb{W})$, and prove that it has a quantum…

We construct explicit local systems on the affine line in characteristic $p>2$, whose geometric monodromy groups are the finite symplectic groups $Sp_{2n}(q)$ for all $n \ge 2$, and others whose geometric monodromy groups are the special…

We construct link invariants using the $D_{2n}$ subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These…

Polynomial Lie (super)algebras $g_{pd}$ are introduced via $G_{i}$-invariant polynomial Jordan maps in quantum composite models with Hamiltonians $H$ having invariance groups $G_{i}$. Algebras $g_{pd}$ have polynomial structure functions in…

The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the $SL_2$ character variety of a topological surface. We realize the skein algebra of the $4$-punctured sphere as the output of a mirror symmetry…

Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M complex Ginibre matrices are distributed according to a determinantal point process. We introduce the notion of a polynomial ensemble and show…

We construct a new family of minimal surfaces of general type with $p_g=q=2$ and $K^2=6$, whose Albanese map is a quadruple cover of an abelian surface with polarization of type $(1,3)$. We also show that this family provides an irreducible…

The 4-dimensional Sklyanin algebra is the homogeneous coordinate ring of a noncommutative analogue of projective 3-space. The degree-two component of the algebra contains a 2-dimensional subspace of central elements. The zero loci of those…

The discussions in the present paper arise from exploring intrinsically the structure nature of the quantum $n$-space. A kind of braided category $\Cal {GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$ is…

Let $\mathcal{A}$ be the group algebra $\mathbf{k}[S_n]$ of the $n$-th symmetric group $S_n$ over a commutative ring $\mathbf{k}$. For any two subsets $A$ and $B$ of $[n]$, we define the elements \[ \nabla_{B,A}:=\sum_{\substack{w\in…

Fix a finite group $G$. We study $\Omega^{SO,G}_2$ and $\Omega^{U,G}_2$, the unitary and oriented bordism groups of smooth $G$-equivariant compact surfaces, respectively, and we calculate them explicitly. Their ranks are determined by the…

The quantum affine $\CU_q (\hat{sl(2)}) $ symmetry is studied when $q^2$ is an even root of unity. The structure of this algebra allows a natural generalization of N=2 supersymmetry algebra. In particular it is found that the momentum…

In this paper we construct a new family of simply connected minimal complex surfaces of general type with $p_g=1$, $q=0$, and $K^2=3, 4, 5, 6, 8$ using a $\mathbb{Q}$-Gorenstein smoothing theory. We also reconstruct minimal complex surfaces…

Kuperberg introduced web spaces for some Lie algebras which are generalizations of the Kauffman bracket skein module on a disk with marked points. We derive some formulas for $A_1$ and $A_2$ clasped web spaces by graphical calculus using…

We use a skein-theoretic version of the Hecke algebras of type A to present three-dimensional diagrammatic views of Gyoja's idempotent elements, based closely on the corresponding Young diagram. In this context we give straightforward…

There is an emerging class of permutation factorization questions that cannot be expressed wholly in terms of the centre of the group algebra of the symmetric group. We shall term these non-central. A notable instance appears in recent work…

We prove full functoriality of Khovanov homology for tangled framed gl2 webs. We use this functoriality result to prove a strong positivity result for (orientable) surface skein algebras. The argument goes categorical and consists in…