Extensions of the constant family of Harish-Chandra pairs of $SL_2(\mathbb{R})$

TL;DR

This paper classifies algebraic families of Harish-Chandra pairs over complex lines, focusing on those with generic fibers isomorphic to the pair associated with SL_2(R), expanding understanding of their algebraic structures.

Contribution

It provides a classification of algebraic families of Harish-Chandra pairs over complex lines with fibers related to SL_2(R), revealing new structural insights.

Findings

Classification of algebraic families over complex lines

Identification of conditions for isomorphism to SL_2(R) pairs

Extension of known Harish-Chandra pair structures

Abstract

We study and classify algebraic families of Harish-Chandra pairs over the complex affine line and over the complex projective line with generic fiber that is isomorphic to the Harish-Chandra pair of $SL_2(\mathbb{R})$.