<p>Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$Y_{1|1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Y</mi> <mrow> <mn>1</mn> <mo stretchy="false">|</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> be the Yangian associated with the general linear Lie superalgebra <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathfrak {gl}_{1|1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="fraktur">gl</mi> <mrow> <mn>1</mn> <mo stretchy="false">|</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>, defined over an algebraically closed field <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\mathbbm {k}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">k</mi> </math></EquationSource> </InlineEquation> of characteristic <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$p>2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>></mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we classify the finite-dimensional irreducible representations of the restricted super-Yangian <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$Y_{1|1}^{[p]}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>Y</mi> <mrow> <mn>1</mn> <mo stretchy="false">|</mo> <mn>1</mn> </mrow> <mrow> <mo stretchy="false">[</mo> <mi>p</mi> <mo stretchy="false">]</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation> and the restricted truncated shifted super-Yangian <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$Y_{1|1,\ell }^{[p]}(\sigma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>Y</mi> <mrow> <mn>1</mn> <mo stretchy="false">|</mo> <mn>1</mn> <mo>,</mo> <mi>ℓ</mi> </mrow> <mrow> <mo stretchy="false">[</mo> <mi>p</mi> <mo stretchy="false">]</mo> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

Representations of the modular shifted super-Yangian $Y_{1|1}(\sigma )$

期刊论文
发表日期：

2026年6月25日

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Hao Chang,
Ruiying Hou,
Hui Wu

摘要

Let $Y_{1|1}$ $Y_{1 | 1}$ be the Yangian associated with the general linear Lie superalgebra $\mathfrak {gl}_{1|1}$ ${gl}_{1 | 1}$ , defined over an algebraically closed field $\mathbbm {k}$ $k$ of characteristic $p>2$ $p > 2$ . In this paper, we classify the finite-dimensional irreducible representations of the restricted super-Yangian $Y_{1|1}^{[p]}$ $Y_{1 | 1}^{[p]}$ and the restricted truncated shifted super-Yangian $Y_{1|1,\ell }^{[p]}(\sigma )$ $Y_{1 | 1, ℓ}^{[p]} (σ)$ .

Representations of the modular shifted super-Yangian \(Y_{1|1}(\sigma )\)

摘要