## 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

SHOWING 1-10 OF 41 REFERENCES

### 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…