Classification on irreducible Whittaker modules over quantum group $${U_q}\left( {{\mathfrak{s}\mathfrak{l}_3},\,{\rm{\Lambda }}} \right)$$
Frontiers of Mathematics in China(2021)
摘要
We define the Whittaker modules over the simply-connected quantum group
$${U_q}\left( {{\mathfrak{s}\mathfrak{l}_3},\,{\rm{\Lambda }}} \right)$$
, where Λ is the weight lattice of Lie algebra
$${\mathfrak{s}\mathfrak{l}_3}$$
. Then we completely classify all those simple ones. Explicitly, a simple Whittaker module over
$${U_q}\left( {{\mathfrak{s}\mathfrak{l}_3},\,{\rm{\Lambda }}} \right)$$
is either a highest weight module, or determined by two parameters z ∈ ℂ and γ ∈ ℂ* (up to a Hopf automorphism).
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关键词
Quantum group, simple, Whittaker module, Whittaker vector, 17B37, 20G42
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