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The space $W$ of $\\pi$ carries a non-degenerate $G$-invariant bilinear form $(\\,,\\,)$ which is unique up to scaling. The form is easily seen to be symmetric or skew-symmetric and we set $\\varepsilon({\\pi})=\\pm 1$ accordingly. In this article, we show that $\\varepsilon{(\\pi)}=1$ when $\\pi$ is a generic representation of $G$ with non-zero vectors fixed under an Iwahori subgroup $I$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.2798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-09-13T07:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"8bb5b0cd0d4dbe8ab6709d33f1b0580709a3246c65835a88e0edea0c4e36efac","abstract_canon_sha256":"e36f3fc05fa6737bf761547c790d076058af0842dc297634762ff493ed288499"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:59.861227Z","signature_b64":"b3f2QSGV7nEPUVmH9ol56P3iDg6ZZT3ektYopuvhFBDF+EYAT8EQNr05fCW5sGhi3RxhV5UumUfxQEhfNXdsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c360ce55bfa5f34ce5a97241239e45624ba83c88ddb56356e55ce919f0837d77","last_reissued_at":"2026-05-18T03:44:59.860460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:59.860460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-dual representations with vectors fixed under an Iwahori subgroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kumar Balasubramanian","submitted_at":"2012-09-13T07:28:54Z","abstract_excerpt":"Let $G$ be the group of $F$-points of a split connected reductive $F$-group over a non-Archimedean local field $F$ of characteristic 0. 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