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Harish-Chandra modules for Yangians
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We study Harish-Chandra representations of the Yangian
Y
(
g
l
2
)
\mathrm {Y}(\mathfrak {gl}_2)
with respect to a natural maximal commutative subalgebra. We prove an analogue of the Kostant theorem showing that the restricted Yangian
Y
p
(
g
l
2
)
\mathrm {Y}_p(\mathfrak {gl}_2)
is a free module over the corresponding subalgebra
Γ
\Gamma
and show that every character of
Γ
\Gamma
defines a finite number of irreducible Harish-Chandra modules over
Y
p
(
g
l
2
)
\mathrm {Y}_p(\mathfrak {gl}_2)
. We study the categories of generic Harish-Chandra modules, describe their simple modules and indecomposable modules in tame blocks.
American Mathematical Society (AMS)
Title: Harish-Chandra modules for Yangians
Description:
We study Harish-Chandra representations of the Yangian
Y
(
g
l
2
)
\mathrm {Y}(\mathfrak {gl}_2)
with respect to a natural maximal commutative subalgebra.
We prove an analogue of the Kostant theorem showing that the restricted Yangian
Y
p
(
g
l
2
)
\mathrm {Y}_p(\mathfrak {gl}_2)
is a free module over the corresponding subalgebra
Γ
\Gamma
and show that every character of
Γ
\Gamma
defines a finite number of irreducible Harish-Chandra modules over
Y
p
(
g
l
2
)
\mathrm {Y}_p(\mathfrak {gl}_2)
.
We study the categories of generic Harish-Chandra modules, describe their simple modules and indecomposable modules in tame blocks.
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