Title: Centralizer construction of the Yangian of the queer Lie superalgebra
Abstract: Consider the complex matrix Lie superalgebra % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj % xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-bc8Njab-vc8Snaa % BaaaleaadaabcaqaaGqaciaa+5eaaiaawIa7aiaad6eaaeqaaaaa!481E! $$ \mathfrak{g}\mathfrak{l}_{\left. N \right|N} $$ with the standard generators E ij where i, j = ±1, . . . , ± N. Define an involutive automorphism η of % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj % xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-bc8Njab-vc8Snaa % BaaaleaadaabcaqaaGqaciaa+5eaaiaawIa7aiaad6eaaeqaaaaa!481E! $$ \mathfrak{g}\mathfrak{l}_{\left. N \right|N} $$ by η(E ij) = E −i,−j . The queer Lie superalgebra qN is the fixed point subalgebra in % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj % xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-bc8Njab-vc8Snaa % BaaaleaadaabcaqaaGqaciaa+5eaaiaawIa7aiaad6eaaeqaaaaa!481E! $$ \mathfrak{g}\mathfrak{l}_{\left. N \right|N} $$ relative to η. Consider the twisted polynomial current Lie superalgebra % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj % xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-bc8Njab-1da9maa % cmaabaacbiGaa4hwamaabmaabaGaa4hDaaGaayjkaiaawMcaaiabgI % Giolab-bc8Njab-vc8SnaaBaaaleaadaabcaqaaiaa+5eaaiaawIa7 % aiaa+5eaaeqaaOWaamWaaeaacaWG0baacaGLBbGaayzxaaGaaiOoai % abeE7aOnaabmaabaGaamiwamaabmaabaGaamiDaaGaayjkaiaawMca % aaGaayjkaiaawMcaaiab-1da9iaa+HfadaqadaqaaGGaciab9jHiTi % aa+rhaaiaawIcacaGLPaaaaiaawUhacaGL9baaaaa!61A9! $$ \mathfrak{g} = \left\{ {X\left( t \right) \in \mathfrak{g}\mathfrak{l}_{\left. N \right|N} \left[ t \right]:\eta \left( {X\left( t \right)} \right) = X\left( { - t} \right)} \right\} $$ . The enveloping algebra U( % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj % xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-bc8Nbaa!42AA! $$ \mathfrak{g} $$ ) of the Lie superalgebra g has a deformation, called the Yangian of qN. For each M = 1,2, . . . , denote by A the centralizer of qM ⊂ q N+M in the associative superalgebra U(q N+M). In this article we construct a sequence of surjective homomorphisms U(qN) ← A ← A 2 ← . . . . We describe the inverse limit of the sequence of centralizer algebras A 1 , A 2 , . . . in terms of the Yangian of qN.