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

Gordan Savin

doi:10.2140/pjm.2026.342.387

April 23, 2026Pacific Journal of MathematicsOpen Access

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

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Key Points

This research aims to establish Howe duality for an exceptional theta correspondence.
Proved Howe duality for the dual pair SL2(ℝ) and F4,1.
Explored K-types of corresponding representations.
Utilized a pair of see-saw identities for the analysis.
Established a relationship between K-types of corresponding representations.
Demonstrated that the theta correspondence satisfies Howe duality.
Showed the effectiveness of see-saw identities in proving these relations.

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Implication

Theorem proves Howe duality in exceptional theta correspondence, indicating relations in K-types.

Abstract

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

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Gordan Savin (2026) studied this question.

synapsesocial.com/papers/69edacbd4a46254e215b4675 https://doi.org/10.2140/pjm.2026.342.387

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

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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