<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> </mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> Fermi-Hubbard gas with three-body losse

We study an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mrow> <a:mi>S</a:mi> <a:mi>U</a:mi> </a:mrow> <a:mo>(</a:mo> <a:mn>3</a:mn> <a:mo>)</a:mo> </a:mrow> </a:math> -invariant Fermi-Hubbard gas undergoing on-site three-body losses. The model presents eight independent strong symmetries preventing the complete depletion of the gas. By making use of a basis of semistandard Young tableaux states, we reveal the presence of a rich phenomenology of stationary states. We classify the latter according to the irreducible representation of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mrow> <b:mi>S</b:mi> <b:mi>U</b:mi> </b:mrow> <b:mo>(</b:mo> <b:mn>3</b:mn> <b:mo>)</b:mo> </b:mrow> </b:math> to which they belong. We finally discuss the presence of three-particle stationary states that are not protected by the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mrow> <c:mi>S</c:mi> <c:mi>U</c:mi> </c:mrow> <c:mo>(</c:mo> <c:mn>3</c:mn> <c:mo>)</c:mo> </c:mrow> </c:math> symmetry.