Towards the theory of Yangians

Abstract

We review the main ideas underlying the emerging theory of Yangians -- the new type of hidden symmetry in string-inspired models. Their classification by quivers is a far-going generalization of simple Lie algebras classification by Dynkin diagrams. However, this is still a kind of project, while a more constructive approach goes through toric Calabi-Yau spaces, related supersymmetric systems and the Duistermaat-Heckmann/equivariant integrals between the fixed points in the ADHM-like moduli spaces. These fixed points are classified by crystals (Young-type diagrams) and Yangian generators describe ``instanton'' transitions between them. Detailed examples will be presented elsewhere.

References in corpus (15)

• Non-Invertible Higher-Categorical Symmetries
• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Crystal Melting and Toric Calabi-Yau Manifolds
• Superintegrability summary
• Shifted Quiver Yangians and Representations from BPS Crystals
• Many-body integrable systems implied by WLZZ models
• Gauge/Bethe correspondence from quiver BPS algebras
• Wall Crossing Invariants: from quantum mechanics to knots
• R-matrix formulation of affine Yangian of $\widehat{\mathfrak{gl}}(1|1)$
• Quiver Yangians and Crystal Melting: A Concise Summary
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
• Defect and degree of the Alexander polynomial
• Evolution properties of the knot's defect

Cited by in corpus (4)

• Simple Representations of BPS Algebras: the case of $Y({\widehat{\mathfrak{gl}}}_2)$
• On character expansion and Gaussian regularization of Itzykson-Zuber measure
• An Overview of Crystals and Double Quiver Yangians
• Vogel's universality and the classification problem for Jacobi identities