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We also prove that the signature of a naturally defined hermitian form on each irreducible representation of $\\check{G}$ can be expressed in terms of these polynomials $P^{\\sigma}_{y,w}(q)$."},"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":"1203.0521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-03-02T17:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"858aa376436c90806d6c91b704f320879a14604661508b1cd7d1e9dc31fabc35","abstract_canon_sha256":"b0d367a3527b266fcc30960cda348442fdc1d80556f38b468f9e59ce0a6edae8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:00.475049Z","signature_b64":"NE045fSiCRMP/J5yzAMSEcEYbdAPAZdTUS1yR8brIK2wU8peuMsRRhrbKGPArxZUDOPhac3KL+df6G/pbflCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bbc2bbbe687edcc38bac3aedaa1b25ad0091b9bda280ca15b8243fa2fa5ea78","last_reissued_at":"2026-05-18T04:01:00.474370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:00.474370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A $(-q)$-analogue of weight multiplicities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"George Lusztig, Zhiwei Yun","submitted_at":"2012-03-02T17:04:45Z","abstract_excerpt":"We prove a conjecture in \\cite{L} stating that certain polynomials $P^{\\sigma}_{y,w}(q)$ introduced in \\cite{LV1} for twisted involutions in an affine Weyl group give $(-q)$-analogues of weight multiplicities of the Langlands dual group $\\check{G}$. 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