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user1832
user1832
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Let $\mathfrak{g}$ be the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$, $K=SO(2)$ the maximal compact subgroup of $SL_2(\mathbb{R})$. Then the classification of irreducible admissible $(\mathfrak{g},K)$-modules is well known.

Now I'm interested in indecomposable $(\mathfrak{g},K)$-modules. After searching the literature, I didn't find anythings, except an old paper by I.M.Gelfand and Ponomarev on indecomposable representations of Lorentz group.

So I'm here wondering if anyone would suggest any reference about indecomposable $(\mathfrak{g},K)$-modules for $SL_2(\mathbb{R})$? Or if this has been done before? Much appreciated for any help.

Let $\mathfrak{g}$ be the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$, $K=SO(2)$ the maximal compact subgroup of $SL_2(\mathbb{R})$. Then the classification of irreducible admissible $(\mathfrak{g},K)$-modules is well known.

Now I'm interested in indecomposable $(\mathfrak{g},K)$-modules. After searching the literature, I didn't find anythings, except an old paper by I.M.Gelfand and Ponomarev on indecomposable representations of Lorentz group.

So I'm here wondering if anyone would suggest any reference about indecomposable $(\mathfrak{g},K)$-modules for $SL_2(\mathbb{R})$? Or if this has been done before? Much appreciated for any help.

Let $\mathfrak{g}$ be the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$, $K=SO(2)$ the maximal compact subgroup of $SL_2(\mathbb{R})$. Then the classification of irreducible admissible $(\mathfrak{g},K)$-modules is well known.

Now I'm interested in indecomposable $(\mathfrak{g},K)$-modules. After searching the literature, I didn't find anythings.

So I'm here wondering if anyone would suggest any reference about indecomposable $(\mathfrak{g},K)$-modules for $SL_2(\mathbb{R})$? Or if this has been done before? Much appreciated for any help.

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user1832
user1832
  • 2.7k
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  • 19
  • 25

reference help indecomposable representations of SL(2,R)

Let $\mathfrak{g}$ be the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$, $K=SO(2)$ the maximal compact subgroup of $SL_2(\mathbb{R})$. Then the classification of irreducible admissible $(\mathfrak{g},K)$-modules is well known.

Now I'm interested in indecomposable $(\mathfrak{g},K)$-modules. After searching the literature, I didn't find anythings, except an old paper by I.M.Gelfand and Ponomarev on indecomposable representations of Lorentz group.

So I'm here wondering if anyone would suggest any reference about indecomposable $(\mathfrak{g},K)$-modules for $SL_2(\mathbb{R})$? Or if this has been done before? Much appreciated for any help.