Open Problems in Geometric Representation Theory

Definitions and mathematical statement

The supplied record contains no recoverable mathematical statement. It is marked statement_status: unrecoverable, has no clean statement, and reproduces a table-of-contents fragment consisting of an isolated word "conjecture", contribution titles, contributor names, page references, and a report header. These elements supply no definite mathematical assertion, hypotheses, domains, boundary conditions, or quantifiers from which definitions and a precise problem can be reconstructed.

In particular, the title "Towards combinatorial invariance for Kazhdan--Lusztig polynomials" does not specify an intended conjecture or its formulation. The other contribution titles likewise do not identify a particular open problem. No contributor listed in this fragment can therefore be assigned as proposer of this registry entry on the supplied evidence.

The registry label open and its dated literature assessment are supplied curation, not a verified assertion that a determinate mathematical problem remains open. A statement-only mathematical draft requires an identifiable problem passage from the cited report; the supplied fragment cannot support one.

Short English statement

This record preserves a table-of-contents fragment, not an identifiable mathematical problem. Its supplied open label does not determine a conjecture. Recovering a precise statement requires the intended problem passage and human mathematical review.

Sources

• Supplied local UnsolvedMath registry record: permanent ID 30004881, exact source problem code catalogue entry, title "Open Problems in Geometric Representation Theory", in the "Oberwolfach Reports Open Problems" collection. The proposer field is unspecified; the proposed-year field is 2021. The original fragment is retained for provenance, with no separate clean statement promoted.
• Supplied report citation: Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891. Supplied source URL and literature-source link, labeled "OWR report": https://doi.org/10.4171/owr/2021/52. The background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature assessment, checked 2026-08-22: status open; the extracted text is another table-of-contents fragment rather than an identifiable mathematical claim, so no determinate resolution can be established. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment or source visit. The supplied background requests independent verification of time-sensitive status and cited claims.
• The supplied statement-verification field describes the official source passage as a table-of-contents fragment containing no mathematical claim. This characterization is supplied provenance and has not been independently verified here.
• Fragment opening: an unidentified entry ending with "conjecture", followed by the page reference 2861. Neither its full title nor its contributor is supplied.
• Geordie Williamson, "Towards combinatorial invariance for Kazhdan--Lusztig polynomials", p. 2863. This is a contents-entry attribution, not an identified problem attribution.
• Olivier Schiffmann, joint with E. Diaconescu, M. Porta, F. Sala and E. Vasserot, "Cohomological Hall algebras of sheaves on surfaces and affine Yangians (in progress)", p. 2866. The qualification "in progress" belongs to the supplied title.
• Ryo Fujita, joint with David Hernandez, "Monoidal Jantzen filtrations for quantum affine algebras", p. 2868.
• Shrawan Kumar, joint with Samuel Jeralds, "Root Components for Tensor Product of Affine Kac--Moody Lie algebra modules", p. 2871.
• Joel Kamnitzer, joint with Ben Webster, Alex Weekes and Oded Yacobi, "Affine Grassmannian slices and categorification", p. 2875.
• Monica Vazirani, joint with Eugene Gorsky and José Simental, "Parabolic Hilbert schemes and rational Cherednik algebra", p. 2875.
• Myungho Kim, joint with Masaki Kashiwara, Se-jin Oh and Euiyong Park, "Monoidal categorification of cluster algebras and quantum affine algebras", p. 2878.
• Alexandre Minets, joint with Ruslan Maksimau, "Semicuspidal categories of affine KLR algebras", p. 2879.
• Bea Schumann, joint with Gleb Koshevoy, "String cones and cluster varieties", p. 2882.
• Catharina Stroppel, joint with Jens Eberhardt, "Motivic Springer Theory", p. 2884.
• The fragment ends with the report header "Enveloping Algebras and Geometric Representation Theory" and page number 2831. The listed titles, collaborations and page references are preserved as supplied; none identifies the intended mathematical target of this registry entry.