Combinatorial Formulae for Nested Bethe Vectors

Abstract

Abstract. We give combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for tensor products of irreducible evaluation modules over the Yangian Y (gl N ) and the quantum affine algebra U q ( gl N ).

Trigonometric weight functions asK-theoretic stable envelope maps for the cotangent bundle of a flag variety

“…Another key novelty of our treatment is Section 6.3 where we will show existence by giving a formula for κ σ ,I . Moreover, this formula for κ σ ,I is a version of the trigonometric weight functions that had appeared in [4,15,5] in hypergeometric solutions of qKZ equations.…”

“…Convenient formulae for the weight functions were suggested in [5]. The weight functions W id,I , I ∈ I λ , in this paper are Laurent polynomials.…”

“…The weight functions W id,I , I ∈ I λ , in this paper are Laurent polynomials. They differ from the corresponding weight functions in [5], that are rational functions, by a common factor independent of I.…”

On Bethe vectors in $$ \mathfrak{g}{\mathfrak{l}}_3 $$-invariant integrable models

“…In the context of the Quantum Inverse Scattering Method (QISM) [6][7][8][9], an algebraic version of this method (NABA) was developed in [10][11][12]. One more approach based on the qKZ equation and Jackson integrals was proposed in [13][14][15] and generalized to the superalgebras in [16]. We should also mention a method to construct Bethe vectors via certain projection of Drinfel'd currents, that was developed in a series of works [17][18][19][20][21].…”

“…Different methods to construct Bethe vectors were developed in [12,[15][16][17]. Several equivalent explicit representations were found in [25].…”