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

Understand

We consider the cotangent bundle $T^*F_\lambda$ of a $GL_n$ partial flag variety, $\lambda=(\lambda_1,...,\lambda_N)$, $|\lambda|=\sum_i\lambda_i=n$, and the torus $T=(\C^\times)^{n+1}$ equivariant K-theory algebra $K_T(T^*F_\lambda)$.

• We introduce K-theoretic stable envelope maps $\Stab_{\sigma}: \oplus_{|\lambda|=n} K_T((T^*F_\lambda)^T)\to\oplus_{|\lambda|=n}K_T(T^*F_\lambda)$, where $\sigma\in S_n$.
• Using these maps we define a quantum loop algebra action on $\oplus_{|\lambda|=n}K_T(T^*F_\lambda)$.
• We describe the associated Bethe algebra $B^q(K_T(T^*F_\lambda))$ by generators and relations in terms of a discrete Wronski map.