Parabolic presentations of the Yangian Y(gl_n)

Abstract

We derive some new presentations for the Yangian associated to the Lie algebra gl_n(C) that are adapted to parabolic subalgebras. At one extreme, the presentation is just the usual RTT presentation, whilst at the other extreme it is a variation on Drinfeld's presentation. All these presentations play an important role in our subsequent article "Shifted Yangians and finite W-algebras".

Minor corrections, some references added. To appear in Commun. Math. Phys

References in corpus (1)

• Hopf structure of the Yangian Y(sl_n) in the Drinfel'd realisation

Cited by in corpus (57)

• Representations of shifted Yangians and finite W-algebras
• Gauss Decomposition of the Yangian Y(gl_{m|n})
• On the R-matrix realization of Yangians and their representations
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• Shuffle algebra realizations of type $A$ super Yangians and quantum affine superalgebras for all Cartan data
• Invariant Differential Operators for Non-Compact Lie Groups: Parabolic Subalgebras
• The trigonometric Casimir connection of a simple Lie algebra
• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
• Equivalences between three presentations of orthogonal and symplectic Yangians
• Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: type C
• Shifted Yangians and finite W-algebras
• The $R$-matrix presentation for the Yangian of a simple Lie algebra
• Elementary invariants for centralizers of nilpotent matrices
• Finite W-superalgebras via super Yangians
• Highest weights for truncated shifted Yangians and product monomial crystals
• Higher Sugawara operators for the quantum affine algebras of type A
• A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
• Structure of the string R-matrix
• On shifted super Yangians and a class of finite W-superalgebras
• Parabolic presentations of the super Yangian $Y({\mathfrak{gl}}_{M|N})$ associated with arbitrary 01-sequences
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• A quantum Mirković-Vybornov isomorphism
• Rational Lax matrices from antidominantly shifted extended Yangians: BCD types
• On the universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)
• Parabolic presentations of the super Yangian $Y(g{l}_{M|N})$
• Gelfand-Tsetlin bases for representations of finite W-algebras and shifted Yangians
• Odd reflections in the Yangian associated with $\mathfrak{g}l(m|n)$
• A Drinfeld-type presentation of the orthosymplectic Yangians
• Representations of the Yangians associated with Lie superalgebras $\mathfrak{osp}(1|2n)$
• Representations of the orthosymplectic Yangian
• Lax matrices from antidominantly shifted Yangians and quantum affine algebras: A-type
• Yangian doubles of classical types and their vertex representations
• Orthosymplectic superoscillator Lax matrices
• Isomorphism between two realizations of the Yangian Y(so_3)
• Drinfeld basis for string-inspired Baxter operators
• Transfer matrices of rational spin chains via novel BGG-type resolutions
• Principal Realization of the Yangian Y(gl(n))
• From Twisted Quantum Loop Algebras to Twisted Yangians
• Isomorphism between twisted $q$-Yangians and affine $ı$quantum groups: type AI
• Affine $ı$quantum groups and twisted Yangians in Drinfeld presentations
• Representations of Quantum Affine Algebras in their $R$-Matrix Realization
• An explicit isomorphism between quantum and classical sl(n)
• Orthosymplectic Yangians
• A Drinfeld type presentation of twisted Yangians
• R-Matrix presentation of quantum affine algebra in type $A_{2n-1}^{(2)}$
• Twisted Yangians and finite W-algebras
• A Recent Look at the Quantum Berezinian in the Yangian Y(gl_{m|n})
• Flag varieties for the Yangian Y(gl_n)
• A note on the quantum Berezinian for the double Yangian of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$
• A Drinfeld presentation for the twisted Yangian $Y_3^{+}$
• Skew representations of twisted Yangians
• Representations of twisted q-Yangians
• Principal realization of twisted Yangians Y(g_N)
• Gaussian generators for the Yangian associated with the Lie superalgebra $\mathfrak{osp}(1|2m)$
• Geometric RTT realization of $U_v(g{l}_n{)}^{+}$
• $RLL$-Realization and Its Hopf Superalgebra Structure of $U_{p,q}(\widehat{\mathfrak{gl}(m|n))}$
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes