14 Citations
Weights of Semiregular Nilpotents in Simple Lie Algebras of D Type
- Mathematics
- 2020
We compute the weights of the adjoint action of semiregular $sl_2$-triples in simple Lie algebras of type $D_n$ using mathematical induction.
Algebraic classical W-algebras and Frobenius manifolds
- MathematicsLetters in Mathematical Physics
- 2021
We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On…
Conjugate Frobenius Manifold and Inversion Symmetry
- MathematicsMathematical Physics, Analysis and Geometry
- 2022
We give a conjugacy relation on certain type of Frobenius manifold structures using the theory of flat pencils of metrics. It leads to a geometric interpretation for the inversion symmetry of…
Local matrix generalizations of $W$-algebras
- Mathematics
- 2014
In this paper, we propose local matrix generalizations of the classical $W$-algebras based on the second Hamiltonian structure of the $\mathcal{Z}_m$-valued KP hierarchy, where $\mathcal{Z}_m$ is a…
Classical r-matrix like approach to Frobenius manifolds, WDVV equations and flat metrics
- Mathematics
- 2015
A general scheme for the construction of flat pencils of contravariant metrics and Frobenius manifolds as well as related solutions to Witten–Dijkgraaf–Verlinde–Verlinde associativity equations is…
Ju n 20 21 Inversion symmetry on Frobenius manifolds June 16 , 2021
- Mathematics
- 2021
We give an interpretation of the inversion symmetry of WDVV equations using theory of flat pencil of metrics associated to Frobenius manifolds. Mathematics Subject Classification (2020) 53D45
Fe b 20 22 Conjugate Frobenius manifold and inversion symmetry February 22 , 2022
- Mathematics
- 2022
We give a conjugacy relation on certain type of Frobenius manifold structures using the theory of flat pencils of metrics. It leads to a geometric interpretation for the inversion symmetry of…
$W$-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions
- Mathematics
- 2009
Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
- Mathematics
- 2022
. We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the…
Classical $W$-algebras and Frobenius manifolds related to Liouville completely integrable systems
- Mathematics
- 2019
We proved that the local bihamiltonian structure obtained by generalized Drinfeld-Sokolov reduction associated to a nilpotent element of semisimple type is reduced by Dirac reduction to the loop…
References
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REMARKS ON BIHAMILTONIAN GEOMETRY AND CLASSICAL W-ALGEBRAS
- Mathematics
- 2009
We obtain a local bihamiltonian structure for any nilpotent element in a simple Lie algebra from the generalized bihamiltonian reduction. We prove that this structure can be obtained by performing…
Simple Singularities and Simple Algebraic Groups
- Mathematics
- 1980
Regular group actions.- Deformation theory.- The quotient of the adjoint action.- The resolution of the adjoint quotient.- Subregular singularities.- Simple singularities.- Nilpotent elements in…
Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures
- Mathematics
- 2007
Introduction to Lie Algebras and Representation Theory
- Mathematics
- 1973
Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-…
The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
- Mathematics
- 1959
Let g be a complex simple Lie algebra and let G be the adjoint group of g. It is by now classical that the Poincare polynomial p G (t) of G factors into the form
Drinfeld-Sokolov reduction on a simple lie algebra from the bihamiltonian point of view
- Mathematics
- 1992
We show that the Drinfeld-Sokolov reduction can be framed in the general theory of bihamiltonian manifolds, with the help of a specialized version of a reduction theorem for Poisson manifolds by…
Lie algebras and equations of Korteweg-de Vries type
- Mathematics
- 1985
The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and…
Geometry of 2D topological field theories
- Mathematics, Physics
- 1994
These lecture notes are devoted to the theory of “equations of associativity” describing geometry of moduli spaces of 2D topological field theories.
TRANSVERSE POISSON STRUCTURES TO ADJOINT ORBITS IN SEMISIMPLE LIE ALGEBRAS
- Mathematics
- 2006
We study the transverse Poisson structure to adjoint orbits in a complex semisimple Lie algebra. The problem is first reduced to the case of nilpotent orbits. We prove then that in suitably chosen…