TY - JOUR

T1 - Algebraic classical W-algebras and Frobenius manifolds

AU - Dinar, Yassir Ibrahim

N1 - Funding Information:
The author thanks Boris Dubrovin for posting him this problem and for encouragement, support and useful discussions. The author also thanks Di Yang for stimulating discussions and anonymous reviewers whose comments/suggestions helped improve and clarify this article. A part of this work was done during the author visits to the Abdus Salam International Centre for Theoretical Physics (ICTP) and the International School for Advanced Studies (SISSA) through the years 2014-2017. This work was also funded by the internal grant of Sultan Qaboos University (IG/SCI/DOMS/15/04).
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2021/10

Y1 - 2021/10

N2 - 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 this space, we construct a local bihamiltonian structure which forms an exact Poisson pencil, defines an algebraic classical W-algebra, admits a dispersionless limit, and its leading term defines an algebraic Frobenius manifold. This leads to a uniform construction of algebraic Frobenius manifolds corresponding to regular cuspidal conjugacy classes in irreducible Weyl groups.

AB - 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 this space, we construct a local bihamiltonian structure which forms an exact Poisson pencil, defines an algebraic classical W-algebra, admits a dispersionless limit, and its leading term defines an algebraic Frobenius manifold. This leads to a uniform construction of algebraic Frobenius manifolds corresponding to regular cuspidal conjugacy classes in irreducible Weyl groups.

KW - Classical W-algebra

KW - Common equilibrium points

KW - Drinfeld–Sokolov reduction

KW - Exact Poisson pencil

KW - Frobenius manifolds

KW - Nilpotent orbits in Lie algebras

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U2 - 10.1007/s11005-021-01458-2

DO - 10.1007/s11005-021-01458-2

M3 - Article

AN - SCOPUS:85114352935

VL - 111

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 5

M1 - 115

ER -