Geodesic
DUALIZING INVOLUTIONS ON THE METAPLECTIC GL(2) à la TUPAN
Glasgow mathematical journal, Tome 63 (2021) no. 2, pp. 426-437

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DOI

Let F be a non-Archimedean local field of characteristic zero. Let G = GL(2, F) and $3\widetildeG = \widetilde{GL}(2,F)$ be the metaplectic group. Let τ be the standard involution on G. A well-known theorem of Gelfand and Kazhdan says that the standard involution takes any irreducible admissible representation of G to its contragredient. In such a case, we say that τ is a dualizing involution. In this paper, we make some modifications and adapt a topological argument of Tupan to the metaplectic group $\widetildeG$ and give an elementary proof that any lift of the standard involution to $\widetildeG$; is also a dualizing involution. 
BALASUBRAMANIAN, KUMAR; TIWARI, EKTA. DUALIZING INVOLUTIONS ON THE METAPLECTIC GL(2) à la TUPAN. Glasgow mathematical journal, Tome 63 (2021) no. 2, pp. 426-437. doi: 10.1017/S0017089520000282
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     title = {DUALIZING {INVOLUTIONS} {ON} {THE} {METAPLECTIC} {GL(2)} \`a la {TUPAN}},
     journal = {Glasgow mathematical journal},
     pages = {426--437},
     year = {2021},
     volume = {63},
     number = {2},
     doi = {10.1017/S0017089520000282},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000282/}
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