Related papers: Comparing invariants of SK1

We study finite-dimensional representations of the Kauffman skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter q is a root of unity. The main one of these…

Feigin-Semikhatov conjecture, now established, states algebraic isomorphisms between the cosets of the subregular $\mathcal{W}$-algebras and the principal $\mathcal{W}$-superalgebras of type A by their full Heisenberg subalgebras. It can be…

In this paper we describe the Seiberg-Witten invariants, which have been introduced by Witten, for manifolds with $b_+=1$. In this case the invariants depend on a chamber structure, and there exists a universal wall crossing formula. For…

We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities with the polyharmonic operator for…

Given a holomorphic vector bundle $E:EX X$ over a compact K\"ahler manifold, one introduces twisted GW-invariants of $X$ replacing virtual fundamental cycles of moduli spaces of stable maps $f: \Sigma \to X$ by their cap-product with a…

We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor $K-$theory. The Milnor $K-$groups can be identified with the top cohomology…

Given a Lie algebra with a scalar product, one may consider the latter as a symplectic structure on a $dg$-scheme, which is the spectrum of the Chevalley--Eilenberg algebra. In the first section we explicitly calculate the first order…

We introduce a class of permutation centralizer algebras which underly the combinatorics of multi-matrix gauge invariant observables. One family of such non-commutative algebras is parametrised by two integers. Its Wedderburn-Artin…

We study the principal subspaces, introduced by B. Feigin and A. Stoyanovsky, of the level 1 standard modules for $\hat{\goth{sl}(l+1)}$ with $l \geq 2$. In this paper we construct exact sequences which give us a complete set of recursions…

We prove the Gan-Gross-Prasad conjecture for $\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$ in general and prove its refinement, namely the Ichino-Ikeda type explicit formula for the central $L$-values, under certain…

For a complex finite-dimensional simple Lie algebra $\mathfrak{g}$, we introduce the notion of Q-datum, which generalizes the notion of a Dynkin quiver with a height function from the viewpoint of Weyl group combinatorics. Using this…

A simple counterexample is presented to a proposition which is used in the arguments given by P. M. Akhmet'ev in his work on the Hopf invariant and Kervaire invariant. The counterexample makes use of the $K$-theory of the quotient of the…

R. Kashaev and N. Reshetikhin introduced the notion of holonomy braiding extending V. Turaev's homotopy braiding to describe the behavior of cyclic representations of the unrestricted quantum group $U_qsl_2$ at root of unity. In this paper,…

We study the representation theory of the type B Schur algebra $\mathcal{L}^n(m)$ with unequal parameters introduced in work of Lai, Nakano and Xiang. For generic values of $q,Q$, this algebra is semi-simple and Morita equivalent to the…

We extend the techniques in arXiv:2209.08865(1) to the non-simply-laced situation, and calculate explicit special values of parabolic affine inverse Kazhdan-Lusztig polynomials for subregular nilpotent orbits. We thus obtain explicit…

We calculate the knot invariant coming from the Teichm\"{u}ller TQFT [AK1]. Specifically we calculate the knot invariant for the complement of the knot $6_1$ both in the original [AK1] and the new formulation of the Teichm\"{u}ller TQFT…

In this manuscript, it is shown that the group of $K_1$-zero-cycles on the second generalized Severi-Brauer variety of an algebra $A$ of index 4 is given by elements of the group $K_1(A)$ together with a square-root of their reduced norm.…

We give Bennequin-Plamenevskaya-Shumakovich type lower bounds for the concordance invariant $s^{\#}$ introduced by Kronheimer and Mrowka. The proof is a consequence of computations for torus knots and the cobordism inequality of $s^{\#}$…

It is a well known result that the number of irreducible representations of SU(N) on a tensor product containing k factors of a vector space V is given by the number of involutions in the symmetric group on k letters. In this paper, we…

We generalize the concepts of weak quantum logarithmic Sobolev inequality (LSI) and weak hypercontractivity (HC), introduced in the quantum setting by Olkiewicz and Zegarlinski, to the case of non-primitive quantum Markov semigroups (QMS).…