ON DONKIN’S TILTING MODULE CONJECTURE I: LOWERING THE PRIME

Christopher P. Bendel; Daniel K. Nakano; Cornelius Pillen; Paul Sobaje

doi:10.1090/ERT/608

ON DONKIN’S TILTING MODULE CONJECTURE I: LOWERING THE PRIME

Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen, Paul Sobaje

Mathematical Sciences

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Abstract

In this paper the authors provide a complete answer to Donkin’s Tilting Module Conjecture for all rank 2 semisimple algebraic groups and SL₄(k) where k is an algebraically closed ﬁeld of characteristic p > 0. In the process, new techniques are introduced involving the existence of (p, r)-ﬁltrations, Lusztig’s character formula, and the G_r T-radical series for baby Verma modules.

Original language	English
Pages (from-to)	455-497
Number of pages	43
Journal	Representation Theory
Volume	26
DOIs	https://doi.org/10.1090/ERT/608
State	Published - 2022

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Mathematics (miscellaneous)

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title = "ON DONKIN{\textquoteright}S TILTING MODULE CONJECTURE I: LOWERING THE PRIME",

abstract = "In this paper the authors provide a complete answer to Donkin{\textquoteright}s Tilting Module Conjecture for all rank 2 semisimple algebraic groups and SL4(k) where k is an algebraically closed ﬁeld of characteristic p > 0. In the process, new techniques are introduced involving the existence of (p, r)-ﬁltrations, Lusztig{\textquoteright}s character formula, and the Gr T-radical series for baby Verma modules.",

author = "Bendel, {Christopher P.} and Nakano, {Daniel K.} and Cornelius Pillen and Paul Sobaje",

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AU - Nakano, Daniel K.

AU - Pillen, Cornelius

AU - Sobaje, Paul

PY - 2022

Y1 - 2022

N2 - In this paper the authors provide a complete answer to Donkin’s Tilting Module Conjecture for all rank 2 semisimple algebraic groups and SL4(k) where k is an algebraically closed ﬁeld of characteristic p > 0. In the process, new techniques are introduced involving the existence of (p, r)-ﬁltrations, Lusztig’s character formula, and the Gr T-radical series for baby Verma modules.

AB - In this paper the authors provide a complete answer to Donkin’s Tilting Module Conjecture for all rank 2 semisimple algebraic groups and SL4(k) where k is an algebraically closed ﬁeld of characteristic p > 0. In the process, new techniques are introduced involving the existence of (p, r)-ﬁltrations, Lusztig’s character formula, and the Gr T-radical series for baby Verma modules.

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DO - 10.1090/ERT/608

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JO - Representation Theory

JF - Representation Theory

ER -

ON DONKIN’S TILTING MODULE CONJECTURE I: LOWERING THE PRIME

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