Untitled

Abstract

Let g be a complex semisimple Lie algebra of rank r, and Y(g) its Yangian [4], a Hopf algebra which contains the universal enveloping algebra U(g) of g as a Hopf subalgebra.Write α 1 , . . . , α r for the fundamental roots and ω 1 , . . . , ω r for the fundamental weights of g. As defined in [6], denote by W m ( ) a particular irreducible Y(g) module, all of whose g-weights λ satisfy λ mω , where α β means β − α is a nonnegative integer linear combination of the roots {α i }. Specifically, W m ( ) decomposes into g-modules aswhere V λ is the irreducible g-module with highest weight λ and it occurs n λ times in W m ( ). In particular, n mω = 1.There is a formula for the multiplicities n λ in [6] based on the conjecture that every finite-dimensional representation of Y(g) can be obtained from one specific representation by means of the "reproduction scheme," defined in [7]. If this conjecture holds, then write λ = mω − n i α i , and it is proved in [6] that n λ = Z( , m|n 1 , . . . , n r ) = partitions n≥1 r k=1 P (k) n (ν) + ν (k) n ν (k) n .(2)

Q-systems as cluster algebras

“…where V (0) is the trivial representation. These modules are also known as fundamental representations of Yangians (or minimal affinizations) and were studied in [1,16].…”

Linear recurrence relations inQ-systems and differenceL-operators

“…In type for some ∈ ⩾  e a 0 . This is argued in theorem 5, [Kle97] for the simply laced case. When t a = 1, p a is actually a polynomial.…”

Development of High Quality 1.36 eV Amorphous SiGe:H Alloy by RF Glow Discharge under Helium Dilution

“…These modules are also known as fundamental representations of Yangians (or minimal affinizations) and were studied in [1,16].…”