Transactions of the Moscow Mathematical Society Template

А. М. Савчук, Андрей Андреевич Шкаликов · 1 Jan 2003

In this paper we propose four different methods to determine Sturm-Liouville operator on an interval $(a,b)$ in case, when a potential $q(x)$ is a distribution from the Sobolev space with negative index of smoothness, i.e. (q\in W_2^{-\theta}), where (\theta\le 1). The main and second terms of asymptotic series for eigenvalues and eigenfunctions of these operators…

Mina Aganagic, Edward Frenkel, Andreĭ Okounkov · 29 Nov 2018

We conjecture, and prove for all simply-laced Lie algebras, an identification between the spaces of $q$-deformed conformal blocks for the deformed ${\mathcal W}$-algebra ${\mathcal W}_{q,t}(\mathfrak {g})$ and quantum affine algebras of $\widehat {^L\mathfrak {g}}$, where $^L\mathfrak {g}$ is the Langlands dual Lie algebra to $\mathfrak {g}$. We argue that this identification may be viewed as…

Andrei Minchenko · 27 Dec 2006

Dynkin classified the maximal semisimple subalgebras of exceptional Lie algebras up to conjugacy, but only classified the simple subalgebras up to the coarser relation of linear conjugacy. In the present paper the simple subalgebras of exceptional Lie algebras are classified up to conjugacy, and their normalizers in the group are found. In a certain sense,…

Alexei Yul’evich Pirkovskii · 1 Jan 2008

We describe and investigate Arens–Michael envelopes of associative algebras and their homological properties. We also introduce and study analytic analogs of some classical ring-theoretic constructs: Ore extensions, Laurent extensions, and tensor algebras. For some finitely generated algebras, we explicitly describe their Arens–Michael envelopes as certain algebras of noncommutative power series, and we also show that…

A. D. Bruno, Irina Goryuchkina · 1 Jan 2010

We obtain all asymptotic expansions of solutions of the sixth Painlev equation near all three singular points x = 0, x = 1, and x = for all values of four complex parameters of this equation. The expansions are obtained for solutions of five types: power, power-logarithmic, complicated, semiexotic, and exotic. They form 117 families.…