SL2-triplet associé à un polynôme homogène.
Smallness problem for quantum affine algebras and quiver varieties
The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...
Sobre derivaciones de algebras de Lie
Sobre derivaciones exteriores de algebras de Lie
Soluble subideals of Lie algebras
Solutions to the XXX type Bethe ansatz equations and flag varieties
We consider a version of the A N Bethe equation of XXX type and introduce a reporduction procedure constructing new solutions of this equation from a given one. The set of all solutions obtained from a given one is called a population. We show that a population is isomorphic to the sl N+1 flag variety and that the populations are in one-to-one correspondence with intersection points of suitable Schubert cycles in a Grassmanian variety. We also obtain similar results for the root systems B N and...
Solvable extensions of a special class of nilpotent Lie algebras
A pair of sequences of nilpotent Lie algebras denoted by and are introduced. Here denotes the dimension of the algebras that are defined for ; the first term in the sequences are denoted by 6.11 and 6.19, respectively, in the standard list of six-dimensional Lie algebras. For each of and all possible solvable extensions are constructed so that and serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program of investigating...
Solvable lattice model and representation theory of quantum affine algebras.
Solvable Lie Algebras and Generalized Cartan Matrices Arising from Isolated Singularities.
Solvable Lie algebras and maximal abelian dimensions.
Some conjectures for Macdonald polynomials of type .
Some constructions in the theory of locally finite simple Lie algebras.
Some counterexamples for infinite dimensional Lie algebras
Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation.
Some division theorems for vector fields
This paper is concerned with the problem of divisibility of vector fields with respect to the Lie bracket [X,Y]. We deal with the local divisibility. The methods used are based on various estimates, in particular those concerning prolongations of dynamical systems. A generalization to polynomials of the adjoint operator (X) is given.
Some examples of nil Lie algebras
Generalizing Petrogradsky’s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand–Kirillov dimension over any field of positive characteristic.
Some exceptional compact matrix pseudogroups
Some lagrangian invariants of symplectic manifolds
The KV-homology theory is a new framework which yields interesting properties of lagrangian foliations. This short note is devoted to relationships between the KV-homology and the KV-cohomology of a lagrangian foliation. Let us denote by (resp. ) the KV-algebra (resp. the space of basic functions) of a lagrangian foliation F. We show that there exists a pairing of cohomology and homology to . That is to say, there is a bilinear map , which is invariant under F-preserving symplectic diffeomorphisms....
Some Lie rings associated with Burnside groups.
Some necessary and sufficient conditions for nilpotent -Lie superalgebras
The paper studies nilpotent -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for -Lie superalgebras which is a generalization of those for -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent -Lie superalgebras and obtain several sufficient conditions for an -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the...