September 28, 2025Open Access

Howe duality for the dual pair SL₂( R) × F4,1: a ping-pong of K-types

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Demonstrates how $K$-types relate under Howe duality for the pair of groups.
Proves the exceptional theta correspondence through advanced pair of identities.
Utilizes see-saw identities to understand the representation connections.
Findings suggest deeper insights into representation theory and dual pairs.

Implication

Analysis reveals how exceptional theta correspondence connects $K$-types in SL2 and F4, indicating new relationships.

Abstract

We prove Howe duality for an exceptional theta correspondence. To that end we exploit a pair of see-saw identities and relate the K-types of corresponding representations.

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Cite This Study

Gordan Savin (2025) studied this question.

synapsesocial.com/papers/68d913a34ddcf71ba560b8c6 https://doi.org/10.48550/arxiv.2508.12534

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Implication

Analysis reveals how exceptional theta correspondence connects $K$-types in SL2 and F4, indicating new relationships.

Abstract

We prove Howe duality for an exceptional theta correspondence. To that end we exploit a pair of see-saw identities and relate the K-types of corresponding representations.

Howe duality for the dual pair SL₂( R) × F4,1: a ping-pong of K-types

Key Points

Implication

Abstract

Discussion

Cite This Study

Howe duality for the dual pair SL₂( R) × F4,1: a ping-pong of K-types

Key Points

Implication

Abstract

Discussion

Cite This Study

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